A373482 Numbers k for which A003415(k) is a multiple of A001414(k), where A003415 is the arithmetic derivative, and A001414 is the sum of prime factors with multiplicity.

1, 4, 6, 8, 9, 10, 14, 15, 16, 21, 22, 25, 26, 27, 32, 33, 34, 35, 36, 38, 39, 46, 49, 51, 55, 57, 58, 62, 64, 65, 69, 72, 74, 77, 81, 82, 85, 86, 87, 91, 93, 94, 95, 100, 106, 111, 112, 115, 118, 119, 121, 122, 123, 125, 126, 128, 129, 133, 134, 141, 142, 143, 145, 146, 155, 156, 158, 159, 161, 166, 169, 177, 178

Offset: 1

Author

Antti Karttunen, Jun 08 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A001414, A003415, A373481 (characteristic function).

After the initial 1, positions of 0's in A373480.

Subsequences: A176540 (k such that A003415(k) = A001414(k)), A346041.

Programs

Mathematica

Select[Range[180],
  Divisible[If[#1 < 2, 0, #1  Total[#2/#1 & @@@ #2]],
    Total[Times @@@ #2]] & @@
  {#, FactorInteger[#]} &] (* Michael De Vlieger, Jun 08 2024 *)

PARI

isA373482 = A373481;