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
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