A324847 Numbers divisible by at least one of their prime indices.

2, 4, 6, 8, 10, 12, 14, 15, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 45, 46, 48, 50, 52, 54, 55, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 75, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 105, 106, 108, 110, 112, 114, 116

Offset

1,1

Comments

A prime index of n is a number m such that prime(m) divides n.

If n is in the sequence, then so are all multiples of n. - Robert Israel, Mar 19 2019

Links

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

Example

The sequence of terms together with their prime indices begins:
   2: {1}
   4: {1,1}
   6: {1,2}
   8: {1,1,1}
  10: {1,3}
  12: {1,1,2}
  14: {1,4}
  15: {2,3}
  16: {1,1,1,1}
  18: {1,2,2}
  20: {1,1,3}
  22: {1,5}
  24: {1,1,1,2}
  26: {1,6}
  28: {1,1,4}
  30: {1,2,3}
  32: {1,1,1,1,1}
  34: {1,7}
  36: {1,1,2,2}

Maple

filter:= proc(n) local F;
  F:= map(numtheory:-pi, numtheory:-factorset(n));
  ormap(t -> n mod t = 0, F);
end proc:
select(filter, [$1..200]); # Robert Israel, Mar 19 2019

Mathematica

Select[Range[100], Or@@Cases[If[#==1, {}, FactorInteger[#]], {p_, _}:>Divisible[#, PrimePi[p]]]&]

Prog

(PARI) isok(n) = {my(f = factor(n)[, 1]); for (k=1, #f, if (!(n % primepi(f[k])), return (1)); ); return (0); } \\ Michel Marcus, Mar 19 2019

Crossrefs

Complement of A324846.

Cf. A003963, A056239, A112798, A120383, A289509, A290822, A304360, A306844.

Cf. A324695, A324741, A324743, A324847, A324756, A324758, A324765, A324848, A324849, A324850, A324852, A324853.

Sequence in context: A336735 A304711 A350803 * A302696 A195125 A228295

Adjacent sequences: A324844 A324845 A324846 * A324848 A324849 A324850

Keyword

nonn

Author

Gus Wiseman, Mar 18 2019

Status

approved