A369969 Numbers that are not multiples of 5, but their arithmetic derivative is.

1, 6, 21, 26, 32, 36, 46, 51, 76, 86, 88, 91, 99, 106, 111, 112, 116, 126, 141, 146, 156, 161, 166, 192, 201, 206, 209, 216, 221, 226, 236, 242, 243, 248, 266, 272, 276, 279, 291, 301, 306, 308, 316, 319, 321, 326, 328, 346, 356, 369, 371, 381, 386, 391, 392, 406, 411, 429, 436, 441, 446, 456, 466, 471, 481, 488, 501

Offset: 1

Author

Antti Karttunen, Feb 10 2024

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A047201 and A327865.

Includes A050997 \ {3125} as a subsequence.

Cf. A003415, A369968 (characteristic function).

Cf. also A046337, A369659, A360110 for cases k=2, 3, 4 of "Nonmultiples of k whose arithmetic derivative is a multiple of k".

Programs

Maple

filter:= proc(n) local F, np, t;
  if n mod 5 = 0 then return false fi;
  F:= ifactors(n)[2];
  np:= add(n*t[2]/t[1],t=F);
  np mod 5 = 0
end proc:
select(filter, [$1..1000]); # Robert Israel, Dec 05 2024

PARI

\\ See A369968.