cp's OEIS Frontend

A307517 Numbers with at least two not necessarily distinct prime factors less than the largest prime factor.

%I A307517 #7 Apr 12 2019 09:14:16
%S A307517 12,20,24,28,30,36,40,42,44,45,48,52,56,60,63,66,68,70,72,76,78,80,84,
%T A307517 88,90,92,96,99,100,102,104,105,108,110,112,114,116,117,120,124,126,
%U A307517 130,132,135,136,138,140,144,148,150,152,153,154,156,160,164,165,168
%N A307517 Numbers with at least two not necessarily distinct prime factors less than the largest prime factor.
%C A307517 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 A307517 The sequence of terms together with their prime indices begins:
%e A307517    12: {1,1,2}
%e A307517    20: {1,1,3}
%e A307517    24: {1,1,1,2}
%e A307517    28: {1,1,4}
%e A307517    30: {1,2,3}
%e A307517    36: {1,1,2,2}
%e A307517    40: {1,1,1,3}
%e A307517    42: {1,2,4}
%e A307517    44: {1,1,5}
%e A307517    45: {2,2,3}
%e A307517    48: {1,1,1,1,2}
%e A307517    52: {1,1,6}
%e A307517    56: {1,1,1,4}
%e A307517    60: {1,1,2,3}
%e A307517    63: {2,2,4}
%e A307517    66: {1,2,5}
%e A307517    68: {1,1,7}
%e A307517    70: {1,3,4}
%e A307517    72: {1,1,1,2,2}
%e A307517    76: {1,1,8}
%p A307517 q:= n-> (l-> add(l[i][2], i=1..nops(l)-1)>1)(sort(ifactors(n)[2])):
%p A307517 select(q, [$1..200])[];  # _Alois P. Heinz_, Apr 12 2019
%t A307517 Select[Range[100],PrimeOmega[#/Power@@FactorInteger[#][[-1]]]>1&]
%Y A307517 Cf. A000094, A000245, A000961, A001222, A052126, A056239, A061395, A064989, A105441, A112798, A243055, A256617, A307516, A325196.
%K A307517 nonn
%O A307517 1,1
%A A307517 _Gus Wiseman_, Apr 12 2019