A344024 a(n) = A003415(A001615(n)).

0, 1, 4, 5, 5, 16, 12, 16, 16, 21, 16, 44, 9, 44, 44, 44, 21, 60, 24, 60, 80, 60, 44, 112, 31, 41, 60, 112, 31, 156, 80, 112, 112, 81, 112, 156, 21, 92, 92, 156, 41, 272, 48, 156, 156, 156, 112, 272, 92, 123, 156, 124, 81, 216, 156, 272, 176, 123, 92, 384, 33, 272, 272, 272, 124, 384, 72, 216, 272, 384, 156, 384, 39, 101

Offset

1,3

Comments

The first nonsquarefree numbers for which this sequence coincides with A342925 are 868, 920, 952, 4260, 4452, 4692, 5060, 5172, ...

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(A005117(n)) = A342925(A005117(n)) for all n.

Mathematica

{0}~Join~Array[If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] &[# Product[1 + 1/p, {p, FactorInteger[#][[All, 1]]}] ] &, 73, 2] (* Michael De Vlieger, May 16 2021 *)

Prog

(PARI)
A001615(n) = if(1==n, n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A344024(n) = A003415(A001615(n));

Crossrefs

Cf. A001615, A003415, A005117.

Cf. also A342925.

Sequence in context: A334018 A154914 A154916 * A327703 A077061 A072508

Adjacent sequences: A344021 A344022 A344023 * A344025 A344026 A344027

Keyword

nonn

Author

Antti Karttunen, May 09 2021

Status

approved