A063977 Numbers which are sums of unitary divisors, the usigma values: their inverse usigma set is not empty; usigma() = A034448().

1, 3, 4, 5, 6, 8, 9, 10, 12, 14, 17, 18, 20, 24, 26, 28, 30, 32, 33, 36, 38, 40, 42, 44, 48, 50, 54, 56, 60, 62, 65, 68, 70, 72, 74, 78, 80, 82, 84, 90, 96, 98, 100, 102, 104, 108, 110, 112, 114, 120, 122, 126, 128, 129, 130, 132, 136, 138, 140, 144, 150, 152, 158

Offset: 1

Author

Labos Elemer, Sep 05 2001

Keywords

• nonn

Links

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

Crossrefs

Cf. A034448, A064000 (complement).

Programs

Mathematica

usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); usigma[1] = 1; seq[max_] := TakeWhile[Union[Array[usigma, max]], # <= max &]; seq[160] (* Amiram Eldar, Jul 22 2024 *)

PARI

usigma(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + f[i, 1]^f[i, 2]);}
lista(nmax) = Set(select(x -> x <= nmax, vector(nmax, i, usigma(i)))); \\ Amiram Eldar, Jul 22 2024