A324562 - OEIS

%I #11 Feb 07 2021 06:25:50

%S 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 35,37,38,39,41,42,43,44,45,46,47,49,50,51,52,53,55,56,57,58,59,61,62,

%U 63,65,66,67,68,69,70,71,73,74,75,76,77,78,79,82,83,84,85

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

%C 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 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 Amiram Eldar, <a href="/A324562/b324562.txt">Table of n, a(n) for n = 1..10000</a>

%F A061395(a(n)) >= A001222(a(n)).

%e The sequence of terms together with their prime indices begins:

%e    2: {1}

%e    3: {2}

%e    5: {3}

%e    6: {1,2}

%e    7: {4}

%e    9: {2,2}

%e   10: {1,3}

%e   11: {5}

%e   13: {6}

%e   14: {1,4}

%e   15: {2,3}

%e   17: {7}

%e   19: {8}

%e   20: {1,1,3}

%e   21: {2,4}

%e   22: {1,5}

%e   23: {9}

%e   25: {3,3}

%e   26: {1,6}

%e   28: {1,1,4}

%p with(numtheory):

%p q:= n-> is(pi(max(factorset(n)))>=bigomega(n)):

%p select(q, [$2..100])[];  # _Alois P. Heinz_, Mar 07 2019

%t Select[Range[2,100],PrimePi[FactorInteger[#][[-1,1]]]>=PrimeOmega[#]&]

%Y Cf. A001222, A003114, A055396, A056239, A061395, A064174, A106529, A112798.

%Y Cf. A324517, A324519, A324521, A324522, A324560, A324562.

%K nonn

%O 1,1

%A _Gus Wiseman_, Mar 06 2019