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A347122 Möbius transform of A347121.

%I A347122 #10 Oct 16 2021 15:22:02
%S A347122 -1,2,3,10,3,24,5,38,29,36,3,90,5,56,61,130,3,152,5,138,95,72,7,306,
%T A347122 57,92,187,214,3,292,7,422,121,108,139,550,5,128,155,474,3,452,5,282,
%U A347122 403,160,7,990,145,348,181,358,7,856,173,734,215,180,3,1046,7,208,625,1330,223,604,5,426,269,700,3,1838,7,236
%N A347122 Möbius transform of A347121.
%H A347122 Antti Karttunen, <a href="/A347122/b347122.txt">Table of n, a(n) for n = 1..10000</a>
%H A347122 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%H A347122 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A347122 a(n) = Sum_{d|n} A008683(n/d) * A347121(d).
%F A347122 a(n) = A347137(n) - 2*A000010(n).
%F A347122 For all n >= 1, a(A000040(n)) = 1 + A001223(n).
%o A347122 (PARI)
%o A347122 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A347122 A347121(n) = (sumdiv(n,d,d*A003961(n/d))-(2*n));
%o A347122 A347122(n) = sumdiv(n,d,moebius(n/d)*A347121(d));
%Y A347122 Cf. A000010, A001223, A003961, A008683, A347121, A347136, A347137.
%K A347122 sign
%O A347122 1,2
%A A347122 _Antti Karttunen_, Aug 24 2021