A328052 Value of sigma(m)/(d(m)*sopf(m)) for the integers m that make this expression an integer.

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

Offset: 1

Author

Michel Marcus, Oct 03 2019

Keywords

• nonn

Examples

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

Links

• Michel Marcus, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Magma

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

Mathematica

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 *)

PARI

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

Formula

a(n) = A000203(A328051(n))/(A000005(A328051(n))*A008472(A328051(n))). - Felix Fröhlich, Oct 03 2019