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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
1, 2, 12, 336, 360, 45696, 52416, 75600, 22665216, 31804416, 42928704, 77792400, 92610000, 164656800, 174636000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 24 22:51 EST 2021. Contains 341592 sequences. (Running on oeis4.)