cp's OEIS Frontend

A324562 Numbers > 1 where the maximum prime index is greater than or equal to the number of prime factors counted with multiplicity.

%I A324562 #11 Feb 07 2021 06:25:50
%S A324562 2,3,5,6,7,9,10,11,13,14,15,17,19,20,21,22,23,25,26,28,29,30,31,33,34,
%T A324562 35,37,38,39,41,42,43,44,45,46,47,49,50,51,52,53,55,56,57,58,59,61,62,
%U A324562 63,65,66,67,68,69,70,71,73,74,75,76,77,78,79,82,83,84,85
%N A324562 Numbers > 1 where the maximum prime index is greater than or equal to the number of prime factors counted with multiplicity.
%C A324562 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 A324562 Also Heinz numbers of the integer partitions enumerated by A064174. The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A324562 Amiram Eldar, <a href="/A324562/b324562.txt">Table of n, a(n) for n = 1..10000</a>
%F A324562 A061395(a(n)) >= A001222(a(n)).
%e A324562 The sequence of terms together with their prime indices begins:
%e A324562    2: {1}
%e A324562    3: {2}
%e A324562    5: {3}
%e A324562    6: {1,2}
%e A324562    7: {4}
%e A324562    9: {2,2}
%e A324562   10: {1,3}
%e A324562   11: {5}
%e A324562   13: {6}
%e A324562   14: {1,4}
%e A324562   15: {2,3}
%e A324562   17: {7}
%e A324562   19: {8}
%e A324562   20: {1,1,3}
%e A324562   21: {2,4}
%e A324562   22: {1,5}
%e A324562   23: {9}
%e A324562   25: {3,3}
%e A324562   26: {1,6}
%e A324562   28: {1,1,4}
%p A324562 with(numtheory):
%p A324562 q:= n-> is(pi(max(factorset(n)))>=bigomega(n)):
%p A324562 select(q, [$2..100])[];  # _Alois P. Heinz_, Mar 07 2019
%t A324562 Select[Range[2,100],PrimePi[FactorInteger[#][[-1,1]]]>=PrimeOmega[#]&]
%Y A324562 Cf. A001222, A003114, A055396, A056239, A061395, A064174, A106529, A112798.
%Y A324562 Cf. A324517, A324519, A324521, A324522, A324560, A324562.
%K A324562 nonn
%O A324562 1,1
%A A324562 _Gus Wiseman_, Mar 06 2019