A003967 - OEIS

%I #22 Feb 11 2022 17:49:04

%S 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,

%T 15,21,29,30,31,6,33,34,35,21,37,38,39,20,41,42,43,33,35,46,47,15,43,

%U 42,51,39,53,30,55,28,57,58,59,45,61,62,49,7,65,66,67,51,69,70,71,28,73

%N Inverse Möbius transform of A003958.

%H Antti Karttunen, <a href="/A003967/b003967.txt">Table of n, a(n) for n = 1..20000</a>

%F 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

%F Dirichlet g.f.: zeta(s) * Product_{p prime} 1 / (1 - p^(1-s) + p^(-s)). - _Ilya Gutkovskiy_, Feb 11 2022

%F Sum_{k=1..n} a(k) ~ Pi^6 * n^2 / (1890 * zeta(3)). - _Vaclav Kotesovec_, Feb 11 2022

%o (PARI)

%o A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };

%o A003967(n) = sumdiv(n,d,A003958(d)); \\ _Antti Karttunen_, Feb 11 2022

%o (PARI) for(n=1, 100, print1(direuler(p=2, n, 1/(1 - X)/(1 - p*X + X))[n], ", ")) \\ _Vaclav Kotesovec_, Feb 11 2022

%Y Cf. A003958, A341635 (Dirichlet inverse).

%K nonn,mult

%O 1,2

%A _Marc LeBrun_

%E More terms from _David W. Wilson_, Aug 29 2001