A341527 - OEIS

%I #15 Feb 17 2021 20:28:52

%S 1,9,10,63,21,5,22,81,325,189,78,35,119,33,7,2511,171,325,115,1323,

%T 220,351,116,45,1519,119,1250,33,465,21,592,2187,260,1539,11,175,779,

%U 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 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 Denominator of ratio A341528(n)/A341529(n). A341526 gives the numerator, see comments there.

%H Antti Karttunen, <a href="/A341527/b341527.txt">Table of n, a(n) for n = 1..8191</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A341529(n) / A341530(n) = A341529(n) / gcd(A341528(n), A341529(n)).

%F For all n > 1, a(n) > A341526(n).

%t 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 (PARI)

%o A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961

%o A341527(n) = { my(s=A003961(n)); denominator((sigma(s)*n)/(sigma(n)*s)); };

%Y Cf. A000203, A003961, A003973, A017665, A017666, A336849, A341525, A341528, A341529, A341530.

%Y Cf. A341526 (numerators).

%Y Cf. A341627 (same sequence as applied onto prime shift array A246278).

%K nonn,frac

%O 1,2

%A _Antti Karttunen_, Feb 16 2021