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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
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
Subsequences: A008864, A181388 \ {0}.
Sequence in context: A197953 A198299 A360948 * A056045 A360794 A220848
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 May 29 14:11 EDT 2024. Contains 372952 sequences. (Running on oeis4.)