A370406 Primitive terms of A370348.

4, 18, 27, 50, 125, 225, 242, 294, 441, 578, 686, 1029, 1089, 1331, 1922, 2401, 2601, 3025, 3362, 3675, 4913, 5070, 5290, 6962, 7225, 7605, 8575, 8649, 8978, 12675, 13182, 13225, 13778, 15129, 15162, 17787, 19773, 21970, 22743, 23762, 23805, 24025, 24334, 29791, 31329, 32258, 32955, 34969, 35378

Offset

1,1

Comments

Terms of A370348 that are not divisible by any other term of A370348.

Numbers k such that there are fewer divisors of prime indices of k than there are prime indices of k, and no proper divisor of k has this property.

Links

Robert Israel, Table of n, a(n) for n = 1..800

Example

a(4) = 50 is a term because the prime indices of 50 = 2*5^2 are 1, 2, 2, and there are 3 of these but only 2 divisors of prime indices, namely 1 and 2, and 50 is not divisible by any of the previous terms 4, 18 and 27 of the sequence.

Maple

filter:= proc(n) uses numtheory; local F, D, t;
  if ormap(t -> n mod t = 0, S) then return false fi;
F:= map(t -> [pi(t[1]), t[2]], ifactors(n)[2]);
D:= `union`(seq(divisors(t[1]), t = F);
nops(D) < add(t[2], t = F);
end proc:
R:= NULL: count:= 0: S:= {}:
for n from 1 while count < 100 do
 if filter(n) then
   R:= R, n; S:= S union {n}; count:= count+1;
 fi
od:
R;

Mathematica

filter[n_] := Module[{F, d},
   If[AnyTrue[S, Mod[n, #] == 0&], Return[False]];
   F = {PrimePi[#[[1]]], #[[2]]} & /@ FactorInteger[n];
   d = Union[Flatten[Divisors /@ F[[All, 1]]]];
   Length[d] < Total[F[[All, 2]]]];
R = {}; count = 0; S = {};
For[n = 1, count < 100, n++, If[filter[n], AppendTo[R, n]; S = Union[S, {n}]; count++]];
R (* Jean-François Alcover, Mar 08 2024, after Robert Israel *)

Crossrefs

Cf. A368110, A370348.

Sequence in context: A323848 A358375 A166749 * A378667 A378633 A103067

Adjacent sequences: A370403 A370404 A370405 * A370407 A370408 A370409

Keyword

nonn

Author

Robert Israel, Feb 17 2024

Status

approved