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

1,2

Links

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

Mathematica

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

Prog

(PARI) isA373482 = A373481;

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.

Sequence in context: A330991 A180366 A340656 * A346041 A341614 A323644

Adjacent sequences: A373479 A373480 A373481 * A373483 A373484 A373485

Keyword

nonn

Author

Antti Karttunen, Jun 08 2024

Status

approved