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A365455
a(n) = sigma(n) / gcd(sigma(n), A156552(2*n)).
3
1, 1, 4, 1, 2, 12, 8, 1, 1, 18, 4, 28, 14, 24, 8, 1, 6, 13, 20, 14, 32, 36, 8, 60, 31, 42, 40, 56, 6, 72, 32, 1, 16, 54, 48, 91, 38, 12, 8, 90, 14, 32, 44, 28, 26, 72, 16, 124, 57, 31, 8, 98, 54, 120, 72, 120, 80, 90, 20, 56, 62, 96, 104, 1, 84, 144, 68, 42, 32, 144, 72, 65, 74, 114, 124, 140, 32, 56, 16, 62, 121, 18
OFFSET
1,3
COMMENTS
Numerator of ratio sigma(n) / A156552(2*n).
FORMULA
a(n) = A000203(n) / A365454(n).
PROG
(PARI)
A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A365455(n) = { my(u=sigma(n)); (u/gcd(u, A156552(2*n))); };
CROSSREFS
Cf. A000203, A028982 (positions of odd terms), A053866 (parity of terms), A156552, A365454, A365456 (denominators).
Sequence in context: A206692 A159756 A110559 * A030441 A298570 A284771
KEYWORD
nonn,frac
AUTHOR
Antti Karttunen, Sep 10 2023
STATUS
approved