A345052 a(n) = A003557(n) * A048250(n) * A173557(n).

1, 3, 8, 6, 24, 24, 48, 12, 24, 72, 120, 48, 168, 144, 192, 24, 288, 72, 360, 144, 384, 360, 528, 96, 120, 504, 72, 288, 840, 576, 960, 48, 960, 864, 1152, 144, 1368, 1080, 1344, 288, 1680, 1152, 1848, 720, 576, 1584, 2208, 192, 336, 360, 2304, 1008, 2808, 216, 2880, 576, 2880, 2520, 3480, 1152, 3720, 2880, 1152, 96

Offset: 1

Author

Antti Karttunen, Jun 08 2021

Keywords

• nonn
• mult
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A003557, A007434, A048250, A065484, A173557, A185197.

Programs

Mathematica

f[p_, e_] := (p^2 - 1)*p^(e - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 16 2022 *)

PARI

A345052(n) = { my(f=factor(n)); prod(i=1, #f~, ((f[i,1]^2)-1)*(f[i,1]^(f[i, 2]-1))); };

Formula

Multiplicative with a(p^e) = (p^2 - 1) * p^(e-1).

a(n) = A007434(n) / A003557(n) = A003557(n) * A048250(n) * A173557(n).

From Amiram Eldar, Oct 16 2022: (Start)

Sum_{k=1..n} a(k) ~ c * n^3, where c = 2/Pi^2 = 0.202642... (A185197).

Sum_{n>=1} 1/a(n) = A065484.

a(n) = A000010(n) * A048250(n). (End)