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

1,2

Links

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

Formula

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

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

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 *)

Prog

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

Crossrefs

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

Cf. also A173557, A347127.

Sequence in context: A255439 A177983 A294673 * A078439 A007063 A335500

Adjacent sequences: A347125 A347126 A347127 * A347129 A347130 A347131

Keyword

nonn,mult,look

Author

Antti Karttunen, Aug 23 2021

Status

approved