OFFSET
1,3
LINKS
FORMULA
a(p^k) = (p - 1)*k where p is a prime and k > 0.
Sum_{k=1..n} a(k) ~ c * n^2, where c = (Pi^4/72) * Product_{p prime} (1 - 4/p^2 + 3/p^3 + 1/p^4 - 1/p^5) = 0.2644703894... . - Amiram Eldar, Nov 30 2022
EXAMPLE
a(60) = a(2^2*3*5) = (2 - 1)*2 * (3 - 1)*1 * (5 - 1)*1 = 16.
MATHEMATICA
a[n_] := Times @@ ((#[[1]] - 1) #[[2]] & /@ FactorInteger[n]); a[1] = 1; Table[a[n], {n, 75}]
Table[EulerPhi[Last[Select[Divisors[n], SquareFreeQ]]] DivisorSigma[0, n/Last[Select[Divisors[n], SquareFreeQ]]], {n, 75}]
PROG
(PARI) a(n)={my(f=factor(n)); prod(i=1, #f~, my(p=f[i, 1], e=f[i, 2]); (p-1)*e)} \\ Andrew Howroyd, Jul 24 2018
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Ilya Gutkovskiy, May 12 2018
STATUS
approved