A347128 a(n) = A018804(n) / A003557(n), where A018804 is Pillai's arithmetical function.

1, 3, 5, 4, 9, 15, 13, 5, 7, 27, 21, 20, 25, 39, 45, 6, 33, 21, 37, 36, 65, 63, 45, 25, 13, 75, 9, 52, 57, 135, 61, 7, 105, 99, 117, 28, 73, 111, 125, 45, 81, 195, 85, 84, 63, 135, 93, 30, 19, 39, 165, 100, 105, 27, 189, 65, 185, 171, 117, 180, 121, 183, 91, 8, 225, 315, 133, 132, 225, 351, 141, 35, 145, 219, 65, 148

Offset: 1

Author

Antti Karttunen, Aug 23 2021

Keywords

• nonn
• mult
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A003557, A018804, A348494 [= gcd(a(n), A342001(n))], A348496 [= gcd(a(n), A347129(n))].

Cf. also A173557, A347127.

Programs

Mathematica

f[p_, e_] := (e*(p - 1)/p + 1)*p^e; A347128[n_] := (Times @@ (f @@@ FactorInteger[n]))/(n/Times @@ (First[Transpose[FactorInteger[n]]]));Table[A347128[n], {n, 1, 76}] (* Robert P. P. McKone, Aug 23 2021, after Amiram Eldar *)

PARI

A347128(n) = { my(f=factor(n)); prod(i=1, #f~, ((f[i, 1]-1)*f[i, 2] + f[i, 1])); };

Formula

Multiplicative with a(p^e) = ((p-1)*e + p).

a(n) = A018804(n) / A003557(n).