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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.
12
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.
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. A341526 (numerators).
Cf. A341627 (same sequence as applied onto prime shift array A246278).
Sequence in context: A271062 A041174 A048070 * A167708 A372764 A135332
KEYWORD
nonn,frac
AUTHOR
Antti Karttunen, Feb 16 2021
STATUS
approved