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%I #7 Apr 12 2019 09:14:16
%S 12,20,24,28,30,36,40,42,44,45,48,52,56,60,63,66,68,70,72,76,78,80,84,
%T 88,90,92,96,99,100,102,104,105,108,110,112,114,116,117,120,124,126,
%U 130,132,135,136,138,140,144,148,150,152,153,154,156,160,164,165,168
%N Numbers with at least two not necessarily distinct prime factors less than the largest prime factor.
%C 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 with at least two not necessarily distinct parts less than the largest part. The enumeration of these partitions by sum is given by A000094.
%e The sequence of terms together with their prime indices begins:
%e 12: {1,1,2}
%e 20: {1,1,3}
%e 24: {1,1,1,2}
%e 28: {1,1,4}
%e 30: {1,2,3}
%e 36: {1,1,2,2}
%e 40: {1,1,1,3}
%e 42: {1,2,4}
%e 44: {1,1,5}
%e 45: {2,2,3}
%e 48: {1,1,1,1,2}
%e 52: {1,1,6}
%e 56: {1,1,1,4}
%e 60: {1,1,2,3}
%e 63: {2,2,4}
%e 66: {1,2,5}
%e 68: {1,1,7}
%e 70: {1,3,4}
%e 72: {1,1,1,2,2}
%e 76: {1,1,8}
%p q:= n-> (l-> add(l[i][2], i=1..nops(l)-1)>1)(sort(ifactors(n)[2])):
%p select(q, [$1..200])[]; # _Alois P. Heinz_, Apr 12 2019
%t Select[Range[100],PrimeOmega[#/Power@@FactorInteger[#][[-1]]]>1&]
%Y Cf. A000094, A000245, A000961, A001222, A052126, A056239, A061395, A064989, A105441, A112798, A243055, A256617, A307516, A325196.
%K nonn
%O 1,1
%A _Gus Wiseman_, Apr 12 2019
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