cp's OEIS Frontend

A324560 Numbers > 1 where the minimum prime index is less than or equal to the number of prime factors counted with multiplicity.

%I A324560 #9 Mar 07 2019 19:59:58
%S A324560 2,4,6,8,9,10,12,14,15,16,18,20,21,22,24,26,27,28,30,32,33,34,36,38,
%T A324560 39,40,42,44,45,46,48,50,51,52,54,56,57,58,60,62,63,64,66,68,69,70,72,
%U A324560 74,75,76,78,80,81,82,84,86,87,88,90,92,93,94,96,98,99,100
%N A324560 Numbers > 1 where the minimum prime index is less than or equal to the number of prime factors counted with multiplicity.
%C A324560 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 A324560 Also Heinz numbers of a certain type of integer partitions counted by A039900 (but not the type of partitions described in the name). The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%F A324560 A055396(a(n)) <= A001222(a(n)).
%e A324560 The sequence of terms together with their prime indices begins:
%e A324560    2: {1}
%e A324560    4: {1,1}
%e A324560    6: {1,2}
%e A324560    8: {1,1,1}
%e A324560    9: {2,2}
%e A324560   10: {1,3}
%e A324560   12: {1,1,2}
%e A324560   14: {1,4}
%e A324560   15: {2,3}
%e A324560   16: {1,1,1,1}
%e A324560   18: {1,2,2}
%e A324560   20: {1,1,3}
%e A324560   21: {2,4}
%e A324560   22: {1,5}
%e A324560   24: {1,1,1,2}
%e A324560   26: {1,6}
%e A324560   27: {2,2,2}
%e A324560   28: {1,1,4}
%e A324560   30: {1,2,3}
%e A324560   32: {1,1,1,1,1}
%p A324560 with(numtheory):
%p A324560 q:= n-> is(pi(min(factorset(n)))<=bigomega(n)):
%p A324560 select(q, [$2..100])[];  # _Alois P. Heinz_, Mar 07 2019
%t A324560 Select[Range[2,100],PrimePi[FactorInteger[#][[1,1]]]<=PrimeOmega[#]&]
%Y A324560 Cf. A001222, A039900, A055396, A056239, A061395, A106529, A112798.
%Y A324560 Cf. A324515, A324517, A324519, A324521, A324522, A324560, A324562.
%K A324560 nonn
%O A324560 1,1
%A A324560 _Gus Wiseman_, Mar 06 2019