A358760 Numbers k for which A349905(k) is a multiple of 4, where A349905(k) is the arithmetic derivative applied to the prime shifted k.

1, 6, 15, 16, 21, 22, 26, 36, 40, 46, 51, 55, 56, 57, 62, 65, 74, 77, 81, 87, 90, 91, 94, 96, 100, 115, 118, 123, 126, 129, 132, 136, 140, 142, 152, 155, 156, 159, 161, 166, 178, 183, 185, 187, 194, 196, 201, 209, 214, 216, 217, 218, 219, 221, 225, 232, 235, 237, 240, 247, 250, 256, 259, 262, 276

Offset: 1

Author

Antti Karttunen, Nov 29 2022

Keywords

• nonn

Comments

Numbers k such that A003961(k) is one of the terms of A327864.

Numbers k such that A001222(k) == A003961(k)-1 (modulo 4).

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A001222, A003415, A003961, A010873, A121262, A246260, A327864, A349905, A358750 (characteristic function).

Setwise difference A028260 \ A358762.

Cf. also A358761, A358763.

Programs

Maple

filter:= proc(n) local m,np,F, F1,F2, i;
  F:= ifactors(n)[2];
  m:= nops(F);
  F1:= map(nextprime, F[..,1]);
  F2:= F[..,2];
  np:= mul(F1[i]^F2[i],i=1..m);
  np*add(F2[i]/F1[i],i=1..m) mod 4 = 0;
end proc:
select(filter, [$1..1000]); # Robert Israel, Nov 29 2023

PARI

isA358760(n) = A358750(n);

Formula

{k | A010873(A349905(k)) = 0}.