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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.
7
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.
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
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, May 19 2019
EXTENSIONS
a(9)-a(15) from Amiram Eldar, Jan 09 2021
STATUS
approved