A374787 Denominator of the mean infinitary abundancy index of the infinitary divisors of n.

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A374784 A374785 A374786 * A374788 A374789 A374790

Keyword

nonn,easy,frac

Author

Amiram Eldar, Jul 20 2024

Status

approved