A264786 Let { d_1, d_2, ..., d_k } be the divisors of n. Then a(n) = d_k^1 + d_(k-1)^2 + ... + d_1^k.

1, 3, 4, 9, 6, 24, 8, 33, 19, 44, 12, 226, 14, 72, 68, 161, 18, 429, 20, 534, 98, 152, 24, 3858, 51, 204, 136, 856, 30, 6534, 32, 1089, 182, 332, 210, 22965, 38, 408, 236, 12886, 42, 14262, 44, 2148, 1868, 584, 48, 128338, 99, 2333, 368, 3214, 54, 21810, 302

Offset: 1

Author

Carlos Eduardo Olivieri, Nov 29 2015

Keywords

• nonn
• easy

Examples

			For n = 4: a(4) = 4^1 + 2^2 + 1^3 = 9.
For n = 5: a(5) = 5^1 + 1^2 = 6.
For n = 6: a(6) = 6^1 + 3^2 + 2^3 + 1^4 = 24.
		

Links

• Carlos Eduardo Olivieri, A polynomial from divisors of n

Crossrefs

Cf. A027750, A180851.

Programs

Mathematica

a[n_] := Sum[Sort[Divisors[n], #1 > #2 &][[i]]^i, {i, DivisorSigma[0, n]}]; Table[a[n], {n, 60}]

PARI

a(n) = my(d = divisors(n)); sum(k=1, #d, d[k]^(#d-k+1)); \\ Michel Marcus, Jan 01 2016