cp's OEIS Frontend

A360668 Numbers > 1 whose greatest prime index is not divisible by their number of prime factors (bigomega).

%I A360668 #9 Feb 18 2023 20:49:42
%S A360668 4,8,10,12,15,16,18,22,24,25,27,28,32,33,34,36,40,42,44,46,48,51,54,
%T A360668 55,60,62,63,64,66,68,69,70,72,76,77,80,81,82,85,88,90,93,94,96,98,99,
%U A360668 100,102,104,105,108,110,112,114,115,116,118,119,120,121,123,124
%N A360668 Numbers > 1 whose greatest prime index is not divisible by their number of prime factors (bigomega).
%C A360668 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%C A360668 Also numbers > 1 whose first differences of 0-prepended prime indices have non-integer mean.
%e A360668 The prime indices of 1617 are {2,4,4,5}, and 5 is not divisible by 4, so 1617 is in the sequence.
%t A360668 Select[Range[2,100],!Divisible[PrimePi[FactorInteger[#][[-1,1]]],PrimeOmega[#]]&]
%Y A360668 These partitions are counted by A200727.
%Y A360668 The complement is A340610 (without 1), counted by A168659.
%Y A360668 For median instead of mean we have A360557, counted by A360691.
%Y A360668 Positions of terms > 1 in A360615 (numerator: A360614).
%Y A360668 A058398 counts partitions by mean, see also A008284, A327482.
%Y A360668 A067340 lists numbers whose prime signature has integer mean.
%Y A360668 A112798 = prime indices, length A001222, sum A056239, mean A326567/A326568.
%Y A360668 A334201 adds up all prime indices except the greatest.
%Y A360668 A348551 = numbers w/ non-integer mean of prime indices, complement A316413.
%Y A360668 Cf. A072978, A078175, A139710, A307683, A359912, A360551, A360554, A360556, A360669.
%K A360668 nonn
%O A360668 1,1
%A A360668 _Gus Wiseman_, Feb 17 2023