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%I #18 Jan 01 2020 08:04:08
%S 2,3,5,7,9,11,13,17,19,23,25,27,29,31,37,41,43,47,49,53,59,61,67,71,
%T 73,79,81,83,89,97,101,103,107,109,113,121,125,127,131,137,139,149,
%U 151,157,163,167,169,173,179,181,191,193,197,199,211,223,227,229,233
%N Heinz numbers of superperiodic integer partitions.
%C First differs from A061345 at a(1) = 2 and next at a(98) = 441.
%C A number n is in the sequence iff n = 2 or the prime indices of n have a common divisor > 1 and the Heinz number of the multiset of prime multiplicities of n, namely A181819(n), is already in the sequence.
%C The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H Vincenzo Librandi, <a href="/A319151/b319151.txt">Table of n, a(n) for n = 1..2326</a>
%e The sequence of partitions whose Heinz numbers belong to the sequence begins: (1), (2), (3), (4), (2,2), (5), (6), (7), (8), (9), (3,3), (2,2,2), (10), (11), (12), (13), (14), (15), (4,4), (16), (17), (18), (19), (20), (21), (22), (2,2,2,2).
%t supperQ[n_]:=Or[n==2,And[GCD@@PrimePi/@FactorInteger[n][[All,1]]>1,supperQ[Times@@Prime/@FactorInteger[n][[All,2]]]]];
%t Select[Range[500],supperQ]
%Y Cf. A001597, A056239, A072774, A098859, A181819, A182850, A289509, A296150, A298748, A304464, A305732, A317246, A317257, A319149, A319152, A319157.
%K nonn
%O 1,1
%A _Gus Wiseman_, Sep 12 2018
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