A324856 Numbers divisible by exactly one of their prime indices.

2, 10, 14, 15, 22, 26, 34, 38, 45, 46, 50, 55, 58, 62, 70, 74, 82, 86, 94, 98, 105, 106, 118, 119, 122, 130, 134, 135, 142, 146, 154, 158, 166, 170, 178, 182, 190, 194, 195, 202, 206, 207, 214, 218, 226, 230, 242, 250, 254, 255, 262, 266, 274, 275, 278, 285

Offset

1,1

Comments

Numbers n such that A324848(n) = 1.

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

If k is in A324846, then k*prime(k) is in the sequence. - Robert Israel, Mar 22 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}
  10: {1,3}
  14: {1,4}
  15: {2,3}
  22: {1,5}
  26: {1,6}
  34: {1,7}
  38: {1,8}
  45: {2,2,3}
  46: {1,9}
  50: {1,3,3}
  55: {3,5}
  58: {1,10}
  62: {1,11}
  70: {1,3,4}
  74: {1,12}
  82: {1,13}
  86: {1,14}
  94: {1,15}
  98: {1,4,4}

Maple

filter:= proc(n) local F;
  F:= select(t -> n mod numtheory:-pi(t[1])=0, ifactors(n)[2]);
  nops(F)=1 and F[1][2]=1
end proc:
select(filter, [$2..1000]); # Robert Israel, Mar 22 2019

Mathematica

Select[Range[100], Total[Cases[If[#==1, {}, FactorInteger[#]], {p_, k_}:>k/; Divisible[#, PrimePi[p]]]]==1&]

Crossrefs

Cf. A000720, A003963, A112798, A120383, A323440, A324694, A324704, A324846, A324847, A324848, A324849, A324850, A324926, A324929.

Sequence in context: A140510 A277087 A098735 * A345017 A349832 A050546

Adjacent sequences: A324853 A324854 A324855 * A324857 A324858 A324859

Keyword

nonn

Author

Gus Wiseman, Mar 21 2019

Status

approved