A374784 Denominator of the mean unitary abundancy index of the unitary divisors of n.

1, 4, 6, 8, 10, 24, 14, 16, 18, 8, 22, 16, 26, 56, 60, 32, 34, 72, 38, 80, 4, 88, 46, 96, 50, 104, 54, 112, 58, 48, 62, 64, 132, 136, 28, 16, 74, 152, 52, 160, 82, 16, 86, 176, 180, 184, 94, 64, 98, 40, 204, 208, 106, 216, 20, 224, 76, 232, 118, 160, 122, 248

Offset: 1

Author

Amiram Eldar, Jul 20 2024

Keywords

• nonn
• easy
• frac

Examples

			For n = 4, 4 has 2 unitary divisors, 1 and 4. Their unitary abundancy indices are usigma(1)/1 = 1 and usigma(4)/4 = 5/4, and their mean unitary abundancy index is (1 + 5/4)/2 = 9/8. Therefore a(4) = denominator(9/8) = 8.
		

Links

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

Crossrefs

Cf. A034444, A034448 (usigma), A077610, A374783 (numerators).

Similar sequences: A374777/A374778, A374786/A374787.

Programs

Mathematica

f[p_, e_] := 1 + 1/(2*p^e); a[1] = 1; a[n_] := Denominator[Times @@ f @@@ FactorInteger[n]]; Array[a, 100]

PARI

a(n) = {my(f = factor(n)); denominator(prod(i = 1, #f~, 1 + 1/(2*f[i,1]^f[i,2])));}