cp's OEIS Frontend

A341527 Denominator of ratio n*sigma(A003961(n)) / sigma(n)*A003961(n), where sigma is the sum of divisors of n, and A003961 shifts the prime factorization of n one step towards larger primes.

%I A341527 #15 Feb 17 2021 20:28:52
%S A341527 1,9,10,63,21,5,22,81,325,189,78,35,119,33,7,2511,171,325,115,1323,
%T A341527 220,351,116,45,1519,119,1250,33,465,21,592,2187,260,1539,11,175,779,
%U A341527 345,1190,1701,903,55,517,27,455,261,424,1395,363,4557,19,833,531,625,117,297,575,4185,1830,147,2077,666,7150,92583,833,195
%N A341527 Denominator of ratio n*sigma(A003961(n)) / sigma(n)*A003961(n), where sigma is the sum of divisors of n, and A003961 shifts the prime factorization of n one step towards larger primes.
%C A341527 Denominator of ratio A341528(n)/A341529(n). A341526 gives the numerator, see comments there.
%H A341527 Antti Karttunen, <a href="/A341527/b341527.txt">Table of n, a(n) for n = 1..8191</a>
%H A341527 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A341527 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A341527 a(n) = A341529(n) / A341530(n) = A341529(n) / gcd(A341528(n), A341529(n)).
%F A341527 For all n > 1, a(n) > A341526(n).
%t A341527 f[p_, e_] := NextPrime[p]^e; g[1] = 1; g[n_] := Times @@ f @@@ FactorInteger[n]; a[n_] := Denominator[n*DivisorSigma[1, (gn = g[n])]/(DivisorSigma[1, n] * gn)]; Array[a, 100] (* _Amiram Eldar_, Feb 17 2021 *)
%o A341527 (PARI)
%o A341527 A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
%o A341527 A341527(n) = { my(s=A003961(n)); denominator((sigma(s)*n)/(sigma(n)*s)); };
%Y A341527 Cf. A000203, A003961, A003973, A017665, A017666, A336849, A341525, A341528, A341529, A341530.
%Y A341527 Cf. A341526 (numerators).
%Y A341527 Cf. A341627 (same sequence as applied onto prime shift array A246278).
%K A341527 nonn,frac
%O A341527 1,2
%A A341527 _Antti Karttunen_, Feb 16 2021