A378436 - OEIS

%I #11 Nov 26 2024 20:59:30

%S 1,2,2,3,2,5,2,4,3,4,2,9,2,4,4,5,2,9,2,7,4,4,2,16,3,4,4,7,2,12,2,6,4,

%T 4,4,21,2,4,4,12,2,11,2,6,6,4,2,28,3,6,4,6,2,14,4,11,4,4,2,53,2,4,6,7,

%U 4,11,2,6,4,8,2,60,2,4,6,6,4,10,2,20,5,4,2,43,4,4,4,9,2,41,4,6,4,4,4,51,2,6,6,12

%N Inverse Möbius transform of A033630, where A033630 is the number of partitions of n into distinct divisors of n.

%C The odd bisection differs from A099774 (the odd bisection of A000005) apparently in the positions given by A005231 (odd abundant numbers): 945, 1575, 2205, 2835, 3465, ...

%H Antti Karttunen, <a href="/A378436/b378436.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = Sum_{d|n} A033630(d).

%o (PARI)

%o A033630(n) = if(!n, 1, my(p=1); fordiv(n, d, p *= (1 + 'x^d)); polcoeff(p, n));

%o A378436(n) = sumdiv(n,d,A033630(d));

%Y Cf. A000005, A005231, A033630, A099774, A378438 (Dirichlet inverse).

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 26 2024