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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: 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

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Last modified May 29 14:11 EDT 2024. Contains 372952 sequences. (Running on oeis4.)