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A349628 Denominators of the Möbius transform of ratio A003961(n)/sigma(n).

%I A349628 #16 Nov 29 2021 14:30:27
%S A349628 1,1,4,7,6,1,8,35,52,1,12,14,14,1,24,155,18,1,20,21,32,1,24,70,186,1,
%T A349628 104,28,30,1,32,217,48,1,16,26,38,1,56,35,42,1,44,42,312,1,48,310,456,
%U A349628 1,72,49,54,1,72,140,80,1,60,84,62,1,416,889,28,1,68,63,96,1,72,26,74,1,744,70,32,1,80,155,968,1,84
%N A349628 Denominators of the Möbius transform of ratio A003961(n)/sigma(n).
%C A349628 Because the ratio A003961(n)/A000203(n) is multiplicative, so is also its Möbius transform. This sequence gives the denominator of that ratio when presented in its lowest terms.
%H A349628 Antti Karttunen, <a href="/A349628/b349628.txt">Table of n, a(n) for n = 1..20000</a>
%H A349628 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A349628 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t A349628 f[p_, e_] := NextPrime[p]^e*(p - 1)/(p^(e + 1) - 1); s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; a[n_] := Denominator @ DivisorSum[n, s[#] * MoebiusMu[n/#] &]; Array[a, 100] (* _Amiram Eldar_, Nov 27 2021 *)
%o A349628 (PARI)
%o A349628 A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
%o A349628 A349628(n) = denominator(sumdiv(n,d,moebius(n/d)*(A003961(d)/sigma(d))));
%Y A349628 Cf. A000203, A003961.
%Y A349628 Cf. A349627 (numerators).
%Y A349628 Cf. also A342671, A349161, A349162, A349634.
%K A349628 nonn,frac
%O A349628 1,3
%A A349628 _Antti Karttunen_, Nov 26 2021