A323440 Numbers divisible by exactly one of their distinct prime indices.

2, 4, 8, 10, 14, 15, 16, 20, 22, 26, 32, 34, 38, 40, 44, 45, 46, 50, 52, 55, 58, 62, 64, 68, 70, 74, 75, 76, 80, 82, 86, 88, 92, 94, 98, 100, 104, 105, 106, 116, 118, 119, 122, 124, 128, 130, 134, 135, 136, 142, 146, 148, 154, 158, 160, 164, 166, 170, 172, 176

Offset

1,1

Comments

Numbers n such that A324852(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.

Links

Amiram Eldar, 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}
   8: {1,1,1}
  10: {1,3}
  14: {1,4}
  15: {2,3}
  16: {1,1,1,1}
  20: {1,1,3}
  22: {1,5}
  26: {1,6}
  32: {1,1,1,1,1}
  34: {1,7}
  38: {1,8}
  40: {1,1,1,3}
  44: {1,1,5}
  45: {2,2,3}
  46: {1,9}
  50: {1,3,3}
  52: {1,1,6}
  55: {3,5}

Mathematica

Select[Range[100], Count[If[#==1, {}, FactorInteger[#]], {p_, _}/; Divisible[#, PrimePi[p]]]==1&]

Prog

(PARI) isok(n) = my(f=factor(n)[, 1]); sum(k=1, #f, (n % primepi(f[k])) == 0) == 1; \\ Michel Marcus, Mar 22 2019

Crossrefs

Cf. A000720, A003963, A112798, A120383, A324704, A324846, A324847, A324848, A324849, A324850, A324856, A324926, A324929.

Sequence in context: A030232 A102024 A104197 * A350804 A285626 A284853

Adjacent sequences: A323437 A323438 A323439 * A323441 A323442 A323443

Keyword

nonn

Author

Gus Wiseman, Mar 21 2019

Status

approved