login
A328052
Value of sigma(m)/(d(m)*sopf(m)) for the integers m that make this expression an integer.
4
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
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
KEYWORD
nonn
AUTHOR
Michel Marcus, Oct 03 2019
STATUS
approved