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

1,2

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.

Links

Table of n, a(n) for n=1..15.

Example

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}

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]

Prog

(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

Crossrefs

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

Sequence in context: A156518 A012727 A296622 * A181142 A088229 A060596

Adjacent sequences: A325753 A325754 A325755 * A325757 A325758 A325759

Keyword

nonn,more

Author

Gus Wiseman, May 19 2019

Extensions

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

Status

approved