A347127 a(n) = A327251(n) / A003557(n).

1, 5, 7, 8, 11, 35, 15, 11, 11, 55, 23, 56, 27, 75, 77, 14, 35, 55, 39, 88, 105, 115, 47, 77, 17, 135, 15, 120, 59, 385, 63, 17, 161, 175, 165, 88, 75, 195, 189, 121, 83, 525, 87, 184, 121, 235, 95, 98, 23, 85, 245, 216, 107, 75, 253, 165, 273, 295, 119, 616, 123, 315, 165, 20, 297, 805, 135, 280, 329, 825, 143, 121

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. A001615, A003557, A327251.

Cf. also A048250, A347128, A347129.

Programs

Mathematica

f[p_, e_] := (p + 1)*e + p; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Aug 24 2021 *)

PARI

A347127(n) = { my(f=factor(n)); prod(i=1, #f~, ((f[i, 1]+1)*f[i, 2] + f[i, 1])); };

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
A003557(n) = (n/factorback(factorint(n)[, 1]));
A327251(n) = sumdiv(n, d, A001615(n/d)*d);
A347127(n) = (A327251(n) / A003557(n));

Formula

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

a(n) = A327251(n) / A003557(n).