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A175317 a(n) = Sum_{d|n} A007955(d) where A007955(m) = product of divisors of m.

%I A175317 #42 Jun 24 2022 20:26:17
%S A175317 1,3,4,11,6,42,8,75,31,108,12,1778,14,206,234,1099,18,5901,20,8116,
%T A175317 452,498,24,333618,131,692,760,22166,30,810372,32,33867,1104,1176,
%U A175317 1238,10085333,38,1466,1538,2568180,42,3112382,44,85690,91386,2142,48,255138610
%N A175317 a(n) = Sum_{d|n} A007955(d) where A007955(m) = product of divisors of m.
%H A175317 Seiichi Manyama, <a href="/A175317/b175317.txt">Table of n, a(n) for n = 1..10000</a>
%F A175317 From _Bernard Schott_, Oct 26 2021: (Start)
%F A175317 a(1) = 1 (the only fixed point).
%F A175317 a(p) = p+1 for prime p only.
%F A175317 a(2^k) = A181388(k+1). (End)
%e A175317 For n = 4, with b(n) = A007955(n), a(4) = b(1) + b(2) + b(4) = 1 + 2 + 8 = 11.
%t A175317 a[n_] := DivisorSum[n, #^(DivisorSigma[0, #]/2) &]; Array[a, 50] (* _Amiram Eldar_, Oct 23 2021 *)
%o A175317 (PARI) a(n) = sumdiv(n, d, vecprod(divisors(d))); \\ _Michel Marcus_, Dec 09 2014 and Oct 23 2021
%o A175317 (Python)
%o A175317 from math import isqrt
%o A175317 from sympy import divisor_count, divisors
%o A175317 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
%Y A175317 Cf. A007429, A007955, A206032, A266265.
%Y A175317 Subsequences: A008864, A181388 \ {0}.
%K A175317 nonn
%O A175317 1,2
%A A175317 _Jaroslav Krizek_, Apr 01 2010
%E A175317 Corrected by _Jaroslav Krizek_, Apr 02 2010
%E A175317 Edited and more terms from _Michel Marcus_, Dec 09 2014