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A346240 Difference between A341512 and its Möbius transform.

%I A346240 #9 Aug 27 2021 05:31:31
%S A346240 0,0,0,1,0,3,0,11,2,3,0,46,0,5,4,85,0,80,0,68,6,3,0,398,2,5,46,130,0,
%T A346240 209,0,575,4,3,6,981,0,5,6,640,0,397,0,182,164,7,0,2830,4,150,4,280,0,
%U A346240 1435,4,1250,6,3,0,2586,0,7,292,3661,6,551,0,368,8,507,0,7983,0,5,212,502,6,847,0,4700,788,3,0,5078,4,5,4,1894
%N A346240 Difference between A341512 and its Möbius transform.
%H A346240 Antti Karttunen, <a href="/A346240/b346240.txt">Table of n, a(n) for n = 1..16384</a>
%H A346240 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A346240 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A346240 a(n) = -Sum_{d|n, d<n} A008683(n/d) * A341512(d).
%F A346240 a(n) = A341512(n) - A346239(n).
%o A346240 (PARI)
%o A346240 A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
%o A346240 A341528(n) = (n*sigma(A003961(n)));
%o A346240 A341529(n) = (sigma(n)*A003961(n));
%o A346240 A341512(n) = (A341529(n)-A341528(n));
%o A346240 A346240(n) = -sumdiv(n,d,(d<n)*moebius(n/d)*A341512(d));
%Y A346240 Cf. A000203, A003961, A008683, A341528, A341529, A341512, A346239.
%Y A346240 Cf. also A347097.
%K A346240 nonn,look
%O A346240 1,6
%A A346240 _Antti Karttunen_, Jul 13 2021