cp's OEIS Frontend

A325755 Numbers n divisible by their prime shadow A181819(n).

%I A325755 #11 Apr 14 2021 05:25:20
%S A325755 1,2,9,12,18,36,40,60,84,112,120,125,132,156,180,204,225,228,250,252,
%T A325755 276,280,336,348,352,360,372,396,440,441,444,450,468,492,516,520,540,
%U A325755 560,564,600,612,636,675,680,684,708,732,760,804,828,832,840,852,876
%N A325755 Numbers n divisible by their prime shadow A181819(n).
%C A325755 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.
%C A325755 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).
%H A325755 Amiram Eldar, <a href="/A325755/b325755.txt">Table of n, a(n) for n = 1..10000</a>
%e A325755 The sequence of terms together with their prime indices begins:
%e A325755      1: {}
%e A325755      2: {1}
%e A325755      9: {2,2}
%e A325755     12: {1,1,2}
%e A325755     18: {1,2,2}
%e A325755     36: {1,1,2,2}
%e A325755     40: {1,1,1,3}
%e A325755     60: {1,1,2,3}
%e A325755     84: {1,1,2,4}
%e A325755    112: {1,1,1,1,4}
%e A325755    120: {1,1,1,2,3}
%e A325755    125: {3,3,3}
%e A325755    132: {1,1,2,5}
%e A325755    156: {1,1,2,6}
%e A325755    180: {1,1,2,2,3}
%e A325755    204: {1,1,2,7}
%e A325755    225: {2,2,3,3}
%e A325755    228: {1,1,2,8}
%e A325755    250: {1,3,3,3}
%e A325755    252: {1,1,2,2,4}
%t A325755 red[n_]:=If[n==1,1,Times@@Prime/@Last/@FactorInteger[n]];
%t A325755 Select[Range[100],Divisible[#,red[#]]&]
%Y A325755 Cf. A181819, A182857, A290689, A290822, A323014, A324843, A325702, A325706, A325708, A325756.
%K A325755 nonn
%O A325755 1,2
%A A325755 _Gus Wiseman_, May 19 2019