A342400 - OEIS

A342400

a(n) is the number of distinct sums of distinct unitary divisors of n.

1, 3, 3, 3, 3, 12, 3, 3, 3, 15, 3, 13, 3, 15, 15, 3, 3, 15, 3, 13, 15, 15, 3, 15, 3, 15, 3, 15, 3, 72, 3, 3, 15, 15, 15, 15, 3, 15, 15, 15, 3, 96, 3, 15, 15, 15, 3, 15, 3, 15, 15, 15, 3, 15, 15, 13, 15, 15, 3, 108, 3, 15, 15, 3, 15, 144, 3, 15, 15, 142, 3, 13

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OFFSET

1,2

LINKS

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

FORMULA

a(n) <= A034448(n) with equality if and only if n is a unitary practical number (A286652).

a(p^e) = 3 for a prime p and e >= 1.

MATHEMATICA

a[n_] := Module[{d = Select[Divisors[n], CoprimeQ[#, n/#] &], x, s, m, c}, m = Length[d]; s = Plus @@ d; c = Rest@CoefficientList[Series[Product[1 + x^d[[i]], {i, 1, m}], {x, 0, s}], x]; Count[c, _?(# > 0 &)]]; Array[a, 100]

CROSSREFS

The unitary version of A119347.

Cf. A034448, A077610, A286652.

Sequence in context: A087575 A001270 A029630 * A349924 A170858 A024725

Adjacent sequences: A342397 A342398 A342399 * A342401 A342402 A342403

KEYWORD

nonn

AUTHOR

Amiram Eldar, Mar 10 2021

STATUS

approved