cp's OEIS Frontend

A324519 Numbers > 1 where the minimum prime index equals the number of prime factors minus the number of distinct prime factors.

%I A324519 #9 Feb 07 2021 06:26:05
%S A324519 4,12,18,20,27,28,44,50,52,60,68,76,84,90,92,98,116,124,126,132,135,
%T A324519 140,148,150,156,164,172,188,189,198,204,212,220,225,228,234,236,242,
%U A324519 244,260,268,276,284,292,294,297,306,308,316,332,338,340,342,348,350
%N A324519 Numbers > 1 where the minimum prime index equals the number of prime factors minus the number of distinct prime factors.
%C A324519 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 A324519 Also Heinz numbers of the integer partitions enumerated by A324520. The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A324519 Amiram Eldar, <a href="/A324519/b324519.txt">Table of n, a(n) for n = 1..10000</a>
%F A324519 A055396(a(n)) = A001222(a(n)) - A001221(a(n)) = A046660(a(n)).
%e A324519 The sequence of terms together with their prime indices begins:
%e A324519    4: {1,1}
%e A324519   12: {1,1,2}
%e A324519   18: {1,2,2}
%e A324519   20: {1,1,3}
%e A324519   27: {2,2,2}
%e A324519   28: {1,1,4}
%e A324519   44: {1,1,5}
%e A324519   50: {1,3,3}
%e A324519   52: {1,1,6}
%e A324519   60: {1,1,2,3}
%e A324519   68: {1,1,7}
%e A324519   76: {1,1,8}
%e A324519   84: {1,1,2,4}
%e A324519   90: {1,2,2,3}
%e A324519   92: {1,1,9}
%e A324519   98: {1,4,4}
%t A324519 Select[Range[2,100],With[{f=FactorInteger[#]},PrimePi[f[[1,1]]]==Total[Last/@f]-Length[f]]&]
%Y A324519 Cf. A001221, A001222, A046660, A055396, A056239, A061395, A106529, A112798.
%Y A324519 Cf. A324515, A324517, A324520, A324521, A324522, A324560, A324562.
%K A324519 nonn
%O A324519 1,1
%A A324519 _Gus Wiseman_, Mar 06 2019