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A165825
Totally multiplicative sequence with a(p) = 4.
14
1, 4, 4, 16, 4, 16, 4, 64, 16, 16, 4, 64, 4, 16, 16, 256, 4, 64, 4, 64, 16, 16, 4, 256, 16, 16, 64, 64, 4, 64, 4, 1024, 16, 16, 16, 256, 4, 16, 16, 256, 4, 64, 4, 64, 64, 16, 4, 1024, 16, 64
OFFSET
1,2
LINKS
FORMULA
a(n) = A000302(A001222(n)) = 4^bigomega(n) = 4^A001222(n).
Dirichlet g.f.: Product_{p prime} 1 / (1 - 4 * p^(-s)). - Ilya Gutkovskiy, Oct 30 2019
Sum_{k=1..n} a(k) = c * n^2 / (2 * log(2)) + O(n * log(n)^3), where c = Product_{p prime > 2} 1 / (1 - 4/p^2) = 2.6413142332392629671869467536904049315527375203817456105081927074458279809... - Vaclav Kotesovec, Feb 17 2022
MATHEMATICA
4^PrimeOmega[Range[100]] (* G. C. Greubel, Apr 09 2016 *)
PROG
(PARI) a(n) = 4^bigomega(n); \\ Altug Alkan, Apr 09 2016
(PARI) for(n=1, 100, print1(direuler(p=2, n, 1/(1 - 4*X))[n], ", ")) \\ Vaclav Kotesovec, Feb 17 2022
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Jaroslav Krizek, Sep 28 2009
STATUS
approved