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A286161
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Compound filter: a(n) = T(A001511(n), A046523(n)), where T(n,k) is sequence A000027 used as a pairing function.
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23
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1, 5, 2, 18, 2, 23, 2, 59, 7, 23, 2, 94, 2, 23, 16, 195, 2, 80, 2, 94, 16, 23, 2, 355, 7, 23, 29, 94, 2, 467, 2, 672, 16, 23, 16, 706, 2, 23, 16, 355, 2, 467, 2, 94, 67, 23, 2, 1331, 7, 80, 16, 94, 2, 302, 16, 355, 16, 23, 2, 1894, 2, 23, 67, 2422, 16, 467, 2, 94, 16, 467, 2, 2779, 2, 23, 67, 94, 16, 467, 2, 1331, 121, 23, 2, 1894, 16, 23, 16, 355, 2, 1832
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OFFSET
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1,2
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..10000
MathWorld, Pairing Function
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FORMULA
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a(n) = (1/2)*(2 + ((A001511(n)+A046523(n))^2) - A001511(n) - 3*A046523(n)).
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PROG
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(PARI)
A001511(n) = (1+valuation(n, 2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ This function from Charles R Greathouse IV, Aug 17 2011
A286161(n) = (2 + ((A001511(n)+A046523(n))^2) - A001511(n) - 3*A046523(n))/2;
for(n=1, 10000, write("b286161.txt", n, " ", A286161(n)));
(Scheme) (define (A286161 n) (* (/ 1 2) (+ (expt (+ (A001511 n) (A046523 n)) 2) (- (A001511 n)) (- (* 3 (A046523 n))) 2)))
(Python)
from sympy import factorint
def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
def P(n):
f = factorint(n)
return sorted([f[i] for i in f])
def a046523(n):
x=1
while True:
if P(n) == P(x): return x
else: x+=1
def a001511(n): return 2 + bin(n - 1)[2:].count("1") - bin(n)[2:].count("1")
def a(n): return T(a001511(n), a046523(n)) # Indranil Ghosh, May 06 2017
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CROSSREFS
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Cf. A000027, A001511, A046523, A286160, A286162, A286163, A286164, A286251.
Sequence in context: A146363 A246797 A087958 * A286252 A286154 A304635
Adjacent sequences: A286158 A286159 A286160 * A286162 A286163 A286164
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, May 04 2017
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STATUS
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approved
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