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A175317 a(n) = Sum_{d|n} A007955(d) where A007955(m) = product of divisors of m. 7
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 (list; graph; refs; listen; history; text; internal format)
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: A328851 A197953 A198299 * A056045 A220848 A232891

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

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Last modified August 18 12:46 EDT 2022. Contains 356212 sequences. (Running on oeis4.)