A324850 Numbers divisible by the product of their prime indices.

1, 2, 4, 6, 8, 12, 16, 24, 28, 30, 32, 36, 48, 56, 60, 64, 72, 96, 112, 120, 128, 144, 152, 156, 168, 180, 192, 216, 224, 240, 256, 288, 304, 312, 330, 336, 360, 384, 432, 448, 476, 480, 512, 576, 608, 624, 660, 672, 720, 768, 784, 828, 840, 848, 864, 888, 896

Offset

1,2

Comments

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, with product A003963(n). For example, the prime indices of 30 are {1,2,3}, with product 6, which divides 30, so 30 is in the sequence.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

n/A003963(n) = A324933(n)/A324934(n).

Example

The sequence of terms together with their prime indices begins:
   1: {}
   2: {1}
   4: {1,1}
   6: {1,2}
   8: {1,1,1}
  12: {1,1,2}
  16: {1,1,1,1}
  24: {1,1,1,2}
  28: {1,1,4}
  30: {1,2,3}
  32: {1,1,1,1,1}
  36: {1,1,2,2}
  48: {1,1,1,1,2}
  56: {1,1,1,4}
  60: {1,1,2,3}
  64: {1,1,1,1,1,1}
  72: {1,1,1,2,2}
  96: {1,1,1,1,1,2}

Mathematica

Select[Range[100], Divisible[#, Times@@Cases[If[#==1, {}, FactorInteger[#]], {p_, k_}:>PrimePi[p]^k]]&]

Prog

(PARI) isok(n) = my(f=factor(n)); !(n % prod(k=1, #f~, primepi(f[k, 1])^f[k, 2])); \\ Michel Marcus, Mar 22 2019

Crossrefs

Cf. A003963, A036844, A120383, A324847, A324756, A324758, A324847, A324848, A324849, A324852, A324853, A324856, A324923, A324924, A324925, A324931.

Sequence in context: A326504 A058629 A323508 * A362804 A095810 A025487

Adjacent sequences: A324847 A324848 A324849 * A324851 A324852 A324853

Keyword

nonn

Author

Gus Wiseman, Mar 18 2019

Status

approved