A325756 A number k belongs to the sequence if k = 1 or k is divisible by its prime shadow A181819(k) and the quotient k/A181819(k) also belongs to the sequence.

1, 2, 12, 336, 360, 45696, 52416, 75600, 22665216, 31804416, 42928704, 77792400, 92610000, 164656800, 174636000

Offset: 1

Author

Gus Wiseman, May 19 2019

Keywords

• nonn
• more

Comments

We define the prime shadow A181819(k) to be the product of primes indexed by the exponents in the prime factorization of n. For example, 90 = prime(1)*prime(2)^2*prime(3) has prime shadow prime(1)*prime(2)*prime(1) = 12.

Examples

			The sequence of terms together with their prime indices begins:
      1: {}
      2: {1}
     12: {1,1,2}
    336: {1,1,1,1,2,4}
    360: {1,1,1,2,2,3}
  45696: {1,1,1,1,1,1,1,2,4,7}
  52416: {1,1,1,1,1,1,2,2,4,6}
  75600: {1,1,1,1,2,2,2,3,3,4}
		

Crossrefs

Cf. A181819, A182857, A290689, A290822, A323014, A324843, A325702, A325706, A325708, A325755.

Programs

Mathematica

red[n_] := If[n == 1, 1, Times @@ Prime /@ Last /@ FactorInteger[n]];
suQ[n_]:=n==1||Divisible[n,red[n]]&&suQ[n/red[n]];
Select[Range[10000],suQ]

PARI

ps(n) = my(f=factor(n)); prod(k=1, #f~, prime(f[k, 2])); \\ A181819
isok(k) = {if ((k==1), return(1)); my(p=ps(k)); ((k % p) == 0) && isok(k/p);} \\ Michel Marcus, Jan 09 2021

Extensions

a(9)-a(15) from Amiram Eldar, Jan 09 2021