A328052 - OEIS

%I #18 Sep 08 2022 08:46:24

%S 1,1,1,3,2,4,2,2,2,2,5,3,2,13,3,3,3,7,5,4,7,4,3,21,13,4,3,8,4,20,9,5,

%T 4,19,5,4,6,8,11,6,6,25,8,6,10,14,5,6,6,25,4,4,6,7,9,10,5,8,26,6,9,8,

%U 10,6,6,6,7,12,6,9,26,19,6,7,10,13,9,9,15,9,7,123

%N Value of sigma(m)/(d(m)*sopf(m)) for the integers m that make this expression an integer.

%H Michel Marcus, <a href="/A328052/b328052.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000203(A328051(n))/(A000005(A328051(n))*A008472(A328051(n))). - _Felix Fröhlich_, Oct 03 2019

%e For A328052(1)=20, sigma(20)/(d(20)*sopf(20)) = 42/(6*7) = 1, so a(1) = 1.

%t f[p_, e_]  := (p^(e + 1) - 1)/((e + 1)*(p - 1)); r[n_] := Times @@ (f @@@ (fct = FactorInteger[n])) / Plus @@ (fct[[;; , 1]]); Select[r /@ Range[2, 4500], IntegerQ] (* _Amiram Eldar_, Oct 03 2019 *)

%o (PARI) lista(nn) = {for (n=2, nn, my(f=factor(n)); if (denominator(q = sigma(f)/(numdiv(f)*sopf(f))) == 1, print1(q, ", ")););}

%o (Magma) [a: k in [2..5000]|IsIntegral(a) where a is DivisorSigma(1,k)/(#Divisors(k)*(&+PrimeDivisors(k)))]; // _Marius A. Burtea_, Oct 03 2019

%Y Cf. A000005, A000203, A008472, A134382, A328051.

%K nonn

%O 1,4

%A _Michel Marcus_, Oct 03 2019