A324560 - OEIS

%I #9 Mar 07 2019 19:59:58

%S 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 39,40,42,44,45,46,48,50,51,52,54,56,57,58,60,62,63,64,66,68,69,70,72,

%U 74,75,76,78,80,81,82,84,86,87,88,90,92,93,94,96,98,99,100

%N Numbers > 1 where the minimum prime index is less 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 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 A055396(a(n)) <= A001222(a(n)).

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

%e    2: {1}

%e    4: {1,1}

%e    6: {1,2}

%e    8: {1,1,1}

%e    9: {2,2}

%e   10: {1,3}

%e   12: {1,1,2}

%e   14: {1,4}

%e   15: {2,3}

%e   16: {1,1,1,1}

%e   18: {1,2,2}

%e   20: {1,1,3}

%e   21: {2,4}

%e   22: {1,5}

%e   24: {1,1,1,2}

%e   26: {1,6}

%e   27: {2,2,2}

%e   28: {1,1,4}

%e   30: {1,2,3}

%e   32: {1,1,1,1,1}

%p with(numtheory):

%p q:= n-> is(pi(min(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, A039900, A055396, A056239, A061395, A106529, A112798.

%Y Cf. A324515, A324517, A324519, A324521, A324522, A324560, A324562.

%K nonn

%O 1,1

%A _Gus Wiseman_, Mar 06 2019