A324501 - OEIS

%I #16 Sep 08 2022 08:46:24

%S 1,3,4,13,6,67,8,105,37,171,12,3433,14,323,346,1681,18,11071,20,14681,

%T 652,771,24,664321,151,1067,1000,38921,30,1681201,32,53793,1552,1803,

%U 1646,20396233,38,2243,2146,4737921,42,6258673,44,146345,143506,3267,48

%N a(n) = numerator of  Sum_{d|n} (1/pod(d)) where pod(k) = the product of the divisors of k (A007955).

%C Sum_{d|n} (1/pod(d)) >= 1 for all n >= 1.

%e Sum_{d|n} (1/pod(d)) for n >= 1: 1, 3/2, 4/3, 13/8, 6/5, 67/36, 8/7, 105/64, 37/27, 171/100, 12/11, 3433/1728, ...

%e For n=4; Sum_{d|4} (1/pod(d)) = 1/pod(1) + 1/pod(2) + 1/pod(4) = (1/1) + (1/2) + (1/8) = 13/8; a(4) = 13.

%t Table[Numerator[Sum[Product[1/d , {d, Divisors[k]}], {k, Divisors[n]}]], {n, 1, 50}] (* _G. C. Greubel_, Mar 04 2019 *)

%o (Magma) [Numerator(&+[1 / &*[c: c in Divisors(d)]: d in Divisors(n)]): n in [1..50]]

%o (PARI) a(n) = numerator(sumdiv(n, d, 1/vecprod(divisors(d)))); \\ _Michel Marcus_, Mar 03 2019

%o (Sage) [sum(product(1/j for j in k.divisors()) for k in n.divisors() ).numerator() for n in (1..50)] # _G. C. Greubel_, Mar 04 2019

%Y Cf. A007955, A324502 (denominators).

%K nonn,frac

%O 1,2

%A _Jaroslav Krizek_, Mar 02 2019