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

1,4

Links

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

Formula

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

Example

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

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 *)

Prog

(PARI) lista(nn) = {for (n=2, nn, my(f=factor(n)); if (denominator(q = sigma(f)/(numdiv(f)*sopf(f))) == 1, print1(q, ", ")); ); }
(Magma) [a: k in [2..5000]|IsIntegral(a) where a is DivisorSigma(1, k)/(#Divisors(k)*(&+PrimeDivisors(k)))]; // Marius A. Burtea, Oct 03 2019

Crossrefs

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

Sequence in context: A073314 A144808 A087023 * A089214 A057038 A175798

Adjacent sequences: A328049 A328050 A328051 * A328053 A328054 A328055

Keyword

nonn

Author

Michel Marcus, Oct 03 2019

Status

approved