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A325755
Numbers n divisible by their prime shadow A181819(n).
32
1, 2, 9, 12, 18, 36, 40, 60, 84, 112, 120, 125, 132, 156, 180, 204, 225, 228, 250, 252, 276, 280, 336, 348, 352, 360, 372, 396, 440, 441, 444, 450, 468, 492, 516, 520, 540, 560, 564, 600, 612, 636, 675, 680, 684, 708, 732, 760, 804, 828, 832, 840, 852, 876
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
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[#]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 19 2019
STATUS
approved