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A347118 Möbius transform of A332449.

%I A347118 #9 Oct 15 2021 21:33:07
%S A347118 1,3,8,6,24,4,48,20,12,8,120,0,168,48,48,60,288,12,360,208,168,72,528,
%T A347118 24,30,312,84,384,840,-32,960,180,312,384,552,108,1368,792,912,480,
%U A347118 1680,-136,1848,1008,-54,912,2208,72,42,18,1224,1200,2808,-4,1080,960,2232,1272,3480,-244,3720,2400,792,540,2832,-120
%N A347118 Möbius transform of A332449.
%H A347118 Antti Karttunen, <a href="/A347118/b347118.txt">Table of n, a(n) for n = 1..10000</a>
%H A347118 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A347118 a(n) = Sum_{d|n} A008683(n/d) * A332449(d).
%o A347118 (PARI)
%o A347118 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A347118 A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
%o A347118 A332449(n) = A005940(1+(3*A156552(n)));
%o A347118 A347118(n) = sumdiv(n,d,moebius(n/d)*A332449(d));
%Y A347118 Cf. A008683, A156552, A332449.
%Y A347118 Cf. also A332463, A347115, A347117.
%K A347118 sign
%O A347118 1,2
%A A347118 _Antti Karttunen_, Aug 21 2021