OFFSET
1,2
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.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of integer partitions containing their multiset of multiplicities as a submultiset (counted by A325702).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
9: {2,2}
12: {1,1,2}
18: {1,2,2}
36: {1,1,2,2}
40: {1,1,1,3}
60: {1,1,2,3}
84: {1,1,2,4}
112: {1,1,1,1,4}
120: {1,1,1,2,3}
125: {3,3,3}
132: {1,1,2,5}
156: {1,1,2,6}
180: {1,1,2,2,3}
204: {1,1,2,7}
225: {2,2,3,3}
228: {1,1,2,8}
250: {1,3,3,3}
252: {1,1,2,2,4}
MATHEMATICA
red[n_]:=If[n==1, 1, Times@@Prime/@Last/@FactorInteger[n]];
Select[Range[100], Divisible[#, red[#]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 19 2019
STATUS
approved