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A346249 Möbius transform of A337549.

%I A346249 #12 Dec 06 2021 11:01:32
%S A346249 0,0,1,2,1,1,3,8,10,1,1,8,3,3,7,28,1,10,3,12,15,1,5,28,16,3,62,24,1,7,
%T A346249 5,92,13,1,21,52,3,3,21,44,1,15,3,24,56,5,5,92,58,16,19,36,5,62,15,84,
%U A346249 27,1,1,44,5,5,108,292,27,13,3,36,37,21,1,168,5,3,68,48,39,21,3,148,346,1,5,84,21,3,31,92,7,56
%N A346249 Möbius transform of A337549.
%H A346249 Antti Karttunen, <a href="/A346249/b346249.txt">Table of n, a(n) for n = 1..20000</a>
%H A346249 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%H A346249 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A346249 a(n) = A008683(n/d) * A337549(d).
%F A346249 a(A000040(n)) = A001223(n)-1. - _Antti Karttunen_, Dec 06 2021
%o A346249 (PARI)
%o A346249 A003972(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); eulerphi(factorback(f)); };
%o A346249 A337549(n) = (A003972(n) - n);
%o A346249 A346249(n) = sumdiv(n,d,moebius(n/d)*A337549(d));
%Y A346249 Cf. A000010, A000040, A001223, A003961, A003972, A008683, A337549.
%Y A346249 Sequences A001359, A029710, A031924 give the subsets of positions of 1's, 3's and 5's in this sequence.
%K A346249 nonn
%O A346249 1,4
%A A346249 _Antti Karttunen_, Jul 14 2021