OFFSET
1,1
COMMENTS
We define the prime shadow A181819(n) 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.
Said differently, these are nonprime numbers > 1 whose prime shadow is a divisor that is either a prime number or a number already in the sequence.
EXAMPLE
The initial terms and their prime indices:
9: {2,2}
36: {1,1,2,2}
125: {3,3,3}
225: {2,2,3,3}
441: {2,2,4,4}
1089: {2,2,5,5}
1260: {1,1,2,2,3,4}
1521: {2,2,6,6}
1980: {1,1,2,2,3,5}
MATHEMATICA
red[n_]:=If[n==1, 1, Times@@Prime/@Last/@FactorInteger[n]];
suQ[n_]:=PrimeQ[n]||Divisible[n, red[n]]&&suQ[red[n]];
Select[Range[2, 2000], suQ[#]&&!PrimeQ[#]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 15 2022
STATUS
approved