A175317 a(n) = Sum_{d|n} A007955(d) where A007955(m) = product of divisors of m.

1, 3, 4, 11, 6, 42, 8, 75, 31, 108, 12, 1778, 14, 206, 234, 1099, 18, 5901, 20, 8116, 452, 498, 24, 333618, 131, 692, 760, 22166, 30, 810372, 32, 33867, 1104, 1176, 1238, 10085333, 38, 1466, 1538, 2568180, 42, 3112382, 44, 85690, 91386, 2142, 48, 255138610

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

From Bernard Schott, Oct 26 2021: (Start)

a(1) = 1 (the only fixed point).

a(p) = p+1 for prime p only.

a(2^k) = A181388(k+1). (End)

Example

For n = 4, with b(n) = A007955(n), a(4) = b(1) + b(2) + b(4) = 1 + 2 + 8 = 11.

Mathematica

a[n_] := DivisorSum[n, #^(DivisorSigma[0, #]/2) &]; Array[a, 50] (* Amiram Eldar, Oct 23 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, vecprod(divisors(d))); \\ Michel Marcus, Dec 09 2014 and Oct 23 2021
(Python)
from math import isqrt
from sympy import divisor_count, divisors
def A175317(n): return sum(isqrt(d)**c if (c:=divisor_count(d)) & 1 else d**(c//2) for d in divisors(n, generator=True)) # Chai Wah Wu, Jun 24 2022

Crossrefs

Cf. A007429, A007955, A206032, A266265.

Subsequences: A008864, A181388 \ {0}.

Sequence in context: A197953 A198299 A360948 * A056045 A360794 A220848

Adjacent sequences: A175314 A175315 A175316 * A175318 A175319 A175320

Keyword

nonn

Author

Jaroslav Krizek, Apr 01 2010

Extensions

Corrected by Jaroslav Krizek, Apr 02 2010

Edited and more terms from Michel Marcus, Dec 09 2014

Status

approved