A329731 Numbers k such that the sum of distinct prime divisors of k divides the sum of unitary divisors of k.

12, 15, 18, 35, 36, 42, 56, 60, 63, 66, 72, 75, 90, 95, 108, 110, 114, 119, 126, 132, 135, 143, 144, 147, 153, 168, 180, 192, 195, 209, 220, 245, 250, 258, 260, 264, 287, 288, 290, 294, 297, 300, 308, 312, 315, 319, 322, 323, 324, 338, 342, 360, 375, 377, 378

Offset

1,1

Comments

The unitary version of A070222.

Links

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

Example

12 is in the sequence since its sum of unitary divisors, 1 + 3 + 4 + 12 = 20, is divisible by its sum of distinct prime divisors, 2 + 3 = 5.

Mathematica

aQ[n_] := Divisible[Times @@ (1 + Power @@@ (f = FactorInteger[n])), Total[First /@ f]]; Select[Range[2, 400], aQ]

Crossrefs

Cf. A008472, A034448, A070222.

Sequence in context: A207830 A348788 A101171 * A350563 A120169 A115349

Adjacent sequences: A329728 A329729 A329730 * A329732 A329733 A329734

Keyword

nonn

Author

Amiram Eldar, Nov 19 2019

Status

approved