A003967 Inverse Möbius transform of A003958.
1, 2, 3, 3, 5, 6, 7, 4, 7, 10, 11, 9, 13, 14, 15, 5, 17, 14, 19, 15, 21, 22, 23, 12, 21, 26, 15, 21, 29, 30, 31, 6, 33, 34, 35, 21, 37, 38, 39, 20, 41, 42, 43, 33, 35, 46, 47, 15, 43, 42, 51, 39, 53, 30, 55, 28, 57, 58, 59, 45, 61, 62, 49, 7, 65, 66, 67, 51, 69, 70, 71, 28, 73
Offset: 1
Links
- Antti Karttunen, Table of n, a(n) for n = 1..20000
Programs
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PARI
A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); }; A003967(n) = sumdiv(n,d,A003958(d)); \\ Antti Karttunen, Feb 11 2022
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PARI
for(n=1, 100, print1(direuler(p=2, n, 1/(1 - X)/(1 - p*X + X))[n], ", ")) \\ Vaclav Kotesovec, Feb 11 2022
Formula
Multiplicative with a(p^e) = e+1 if p = 2; ((p-1)^(e+1)-1)/(p-2) if p > 2. - David W. Wilson, Sep 01 2001
Dirichlet g.f.: zeta(s) * Product_{p prime} 1 / (1 - p^(1-s) + p^(-s)). - Ilya Gutkovskiy, Feb 11 2022
Sum_{k=1..n} a(k) ~ Pi^6 * n^2 / (1890 * zeta(3)). - Vaclav Kotesovec, Feb 11 2022
Extensions
More terms from David W. Wilson, Aug 29 2001