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

1,2

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

Formula

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

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

Prog

(PARI) isA358760(n) = A358750(n);

Crossrefs

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

Setwise difference A028260 \ A358762.

Cf. also A358761, A358763.

Sequence in context: A199223 A199094 A009579 * A114812 A158338 A351472

Adjacent sequences: A358757 A358758 A358759 * A358761 A358762 A358763

Keyword

nonn

Author

Antti Karttunen, Nov 29 2022

Status

approved