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A175317
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a(n) = Sum_{d|n} A007955(d) where A007955(m) = product of divisors of m.
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7
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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
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 1..10000
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FORMULA
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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)
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EXAMPLE
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For n = 4, with b(n) = A007955(n), a(4) = b(1) + b(2) + b(4) = 1 + 2 + 8 = 11.
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MATHEMATICA
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a[n_] := DivisorSum[n, #^(DivisorSigma[0, #]/2) &]; Array[a, 50] (* Amiram Eldar, Oct 23 2021 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Jaroslav Krizek, Apr 01 2010
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EXTENSIONS
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Corrected by Jaroslav Krizek, Apr 02 2010
Edited and more terms from Michel Marcus, Dec 09 2014
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STATUS
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approved
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