cp's OEIS Frontend

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.

%I A325756 #13 Jan 09 2021 11:06:14
%S A325756 1,2,12,336,360,45696,52416,75600,22665216,31804416,42928704,77792400,
%T A325756 92610000,164656800,174636000
%N 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.
%C A325756 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.
%e A325756 The sequence of terms together with their prime indices begins:
%e A325756       1: {}
%e A325756       2: {1}
%e A325756      12: {1,1,2}
%e A325756     336: {1,1,1,1,2,4}
%e A325756     360: {1,1,1,2,2,3}
%e A325756   45696: {1,1,1,1,1,1,1,2,4,7}
%e A325756   52416: {1,1,1,1,1,1,2,2,4,6}
%e A325756   75600: {1,1,1,1,2,2,2,3,3,4}
%t A325756 red[n_] := If[n == 1, 1, Times @@ Prime /@ Last /@ FactorInteger[n]];
%t A325756 suQ[n_]:=n==1||Divisible[n,red[n]]&&suQ[n/red[n]];
%t A325756 Select[Range[10000],suQ]
%o A325756 (PARI) ps(n) = my(f=factor(n)); prod(k=1, #f~, prime(f[k, 2])); \\ A181819
%o A325756 isok(k) = {if ((k==1), return(1)); my(p=ps(k)); ((k % p) == 0) && isok(k/p);} \\ _Michel Marcus_, Jan 09 2021
%Y A325756 Cf. A181819, A182857, A290689, A290822, A323014, A324843, A325702, A325706, A325708, A325755.
%K A325756 nonn,more
%O A325756 1,2
%A A325756 _Gus Wiseman_, May 19 2019
%E A325756 a(9)-a(15) from _Amiram Eldar_, Jan 09 2021