cp's OEIS Frontend

A324522 Numbers > 1 where the minimum prime index is equal to the number of prime factors counted with multiplicity.

%I A324522 #9 Mar 10 2019 19:19:13
%S A324522 2,9,15,21,33,39,51,57,69,87,93,111,123,125,129,141,159,175,177,183,
%T A324522 201,213,219,237,245,249,267,275,291,303,309,321,325,327,339,381,385,
%U A324522 393,411,417,425,447,453,455,471,475,489,501,519,537,543,573,575,579,591
%N A324522 Numbers > 1 where the minimum prime index is equal to the number of prime factors counted with multiplicity.
%C A324522 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 A324522 Also Heinz numbers of integer partitions where the minimum part is equal to the number of parts (A006141). The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A324522 Alois P. Heinz, <a href="/A324522/b324522.txt">Table of n, a(n) for n = 1..10000</a>
%F A324522 A055396(a(n)) = A001222(a(n)).
%e A324522 The sequence of terms together with their prime indices begins:
%e A324522     2: {1}
%e A324522     9: {2,2}
%e A324522    15: {2,3}
%e A324522    21: {2,4}
%e A324522    33: {2,5}
%e A324522    39: {2,6}
%e A324522    51: {2,7}
%e A324522    57: {2,8}
%e A324522    69: {2,9}
%e A324522    87: {2,10}
%e A324522    93: {2,11}
%e A324522   111: {2,12}
%e A324522   123: {2,13}
%e A324522   125: {3,3,3}
%e A324522   129: {2,14}
%e A324522   141: {2,15}
%e A324522   159: {2,16}
%e A324522   175: {3,3,4}
%p A324522 with(numtheory):
%p A324522 q:= n-> is(pi(min(factorset(n)))=bigomega(n)):
%p A324522 select(q, [$2..600])[];  # _Alois P. Heinz_, Mar 07 2019
%t A324522 Select[Range[2,100],PrimePi[FactorInteger[#][[1,1]]]==PrimeOmega[#]&]
%Y A324522 Cf. A001222, A006141, A055396, A056239, A106529, A112798, A256617.
%Y A324522 Cf. A324515, A324517, A324519, A324521, A324522, A324560, A324562.
%K A324522 nonn
%O A324522 1,1
%A A324522 _Gus Wiseman_, Mar 06 2019