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.

1, 9, 10, 63, 21, 5, 22, 81, 325, 189, 78, 35, 119, 33, 7, 2511, 171, 325, 115, 1323, 220, 351, 116, 45, 1519, 119, 1250, 33, 465, 21, 592, 2187, 260, 1539, 11, 175, 779, 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

Offset

1,2

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..8191

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

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

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

Mathematica

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 *)

Prog

(PARI)
A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A341527(n) = { my(s=A003961(n)); denominator((sigma(s)*n)/(sigma(n)*s)); };

Crossrefs

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

Cf. A341526 (numerators).

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

Sequence in context: A271062 A041174 A048070 * A167708 A372764 A135332

Adjacent sequences: A341524 A341525 A341526 * A341528 A341529 A341530

Keyword

nonn,frac

Author

Antti Karttunen, Feb 16 2021

Status

approved