login
A374784
Denominator of the mean unitary abundancy index of the unitary divisors of n.
5
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
1,2
LINKS
EXAMPLE
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.
MATHEMATICA
f[p_, e_] := 1 + 1/(2*p^e); a[1] = 1; a[n_] := Denominator[Times @@ f @@@ FactorInteger[n]]; Array[a, 100]
PROG
(PARI) a(n) = {my(f = factor(n)); denominator(prod(i = 1, #f~, 1 + 1/(2*f[i, 1]^f[i, 2]))); }
CROSSREFS
Cf. A034444, A034448 (usigma), A077610, A374783 (numerators).
Similar sequences: A374777/A374778, A374786/A374787.
Sequence in context: A369139 A294243 A349694 * A298473 A374787 A054284
KEYWORD
nonn,easy,frac
AUTHOR
Amiram Eldar, Jul 20 2024
STATUS
approved