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A374787
Denominator of the mean infinitary abundancy index of the infinitary divisors of n.
5
1, 4, 6, 8, 10, 24, 14, 32, 18, 8, 22, 16, 26, 56, 60, 32, 34, 72, 38, 80, 4, 88, 46, 64, 50, 104, 108, 112, 58, 48, 62, 128, 132, 136, 28, 16, 74, 152, 52, 64, 82, 16, 86, 176, 180, 184, 94, 64, 98, 40, 204, 208, 106, 432, 20, 448, 76, 232, 118, 160, 122, 248
OFFSET
1,2
LINKS
EXAMPLE
For n = 4, 4 has 2 infinitary divisors, 1 and 4. Their infinitary abundancy indices are isigma(1)/1 = 1 and isigma(4)/4 = 5/4, and their mean infinitary abundancy index is (1 + 5/4)/2 = 9/8. Therefore a(4) = denominator(9/8) = 8.
MATHEMATICA
f[p_, e_] := p^(2^(-1 + Position[Reverse@IntegerDigits[e, 2], _?(# == 1 &)])); a[1] = 1; a[n_] := Denominator[Times @@ (1 + 1/(2*Flatten@ (f @@@ FactorInteger[n])))]; Array[a, 100]
PROG
(PARI) a(n) = {my(f = factor(n), b); denominator(prod(i = 1, #f~, b = binary(f[i, 2]); prod(k=1, #b, if(b[k], 1 + 1/(2*f[i, 1]^(2^(#b-k))), 1)))); }
CROSSREFS
Cf. A037445, A049417 (isigma), A077609, A374786 (numerators).
Similar sequences: A374777/A374778, A374783/A374784.
Sequence in context: A349694 A374784 A298473 * A054284 A295287 A351758
KEYWORD
nonn,easy,frac
AUTHOR
Amiram Eldar, Jul 20 2024
STATUS
approved