OFFSET
1,2
COMMENTS
The unitary analog of A060640.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..20000
FORMULA
a(n) = Sum_{d|n, gcd(d, n/d) = 1} d * usigma(n/d).
a(n) = Sum_{d|n, gcd(d, n/d) = 1} d * 2^omega(d).
Dirichlet g.f.: zeta(s-1) * zeta(s) * Product_{p prime} (1 + 1/p^(s-1) - 2/p^(2*s-1)). - Amiram Eldar, Jul 24 2024
MAPLE
a:= n-> mul(2*i[1]^i[2]+1, i=ifactors(n)[2]):
seq(a(n), n=1..80); # Alois P. Heinz, Apr 18 2021
MATHEMATICA
a[1] = 1; a[n_] := Times @@ ((2 #[[1]]^#[[2]] + 1) & /@ FactorInteger[n]); Table[a[n], {n, 66}]
PROG
(PARI) a(n) = my(f=factor(n)); for (k=1, #f~, f[k, 1] = 2*f[k, 1]^f[k, 2]+1; f[k, 2]=1); factorback(f); \\ Michel Marcus, Apr 18 2021
CROSSREFS
KEYWORD
AUTHOR
Ilya Gutkovskiy, Apr 18 2021
STATUS
approved