login
A003967
Inverse Möbius transform of A003958.
2
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
1,2
LINKS
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
PROG
(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
(PARI) for(n=1, 100, print1(direuler(p=2, n, 1/(1 - X)/(1 - p*X + X))[n], ", ")) \\ Vaclav Kotesovec, Feb 11 2022
CROSSREFS
Cf. A003958, A341635 (Dirichlet inverse).
Sequence in context: A366418 A328745 A357134 * A349390 A099209 A099208
KEYWORD
nonn,mult
AUTHOR
EXTENSIONS
More terms from David W. Wilson, Aug 29 2001
STATUS
approved