cp's OEIS Frontend

A327900 Nonprime squarefree numbers whose prime indices all have the same Omega (number of prime factors counted with multiplicity).

%I A327900 #5 Oct 01 2019 09:48:42
%S A327900 1,15,33,51,55,85,91,93,123,155,161,165,177,187,201,203,205,249,255,
%T A327900 295,299,301,327,329,335,341,377,381,415,451,465,471,511,527,537,545,
%U A327900 553,559,561,573,611,615,633,635,649,667,679,697,703,707,723,737,785,831
%N A327900 Nonprime squarefree numbers whose prime indices all have the same Omega (number of prime factors counted with multiplicity).
%C A327900 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.
%H A327900 Gus Wiseman, <a href="/A038041/a038041.txt">Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.</a>
%e A327900 The sequence of terms together with their prime indices begins:
%e A327900     1: {}
%e A327900    15: {2,3}
%e A327900    33: {2,5}
%e A327900    51: {2,7}
%e A327900    55: {3,5}
%e A327900    85: {3,7}
%e A327900    91: {4,6}
%e A327900    93: {2,11}
%e A327900   123: {2,13}
%e A327900   155: {3,11}
%e A327900   161: {4,9}
%e A327900   165: {2,3,5}
%e A327900   177: {2,17}
%e A327900   187: {5,7}
%e A327900   201: {2,19}
%e A327900   203: {4,10}
%e A327900   205: {3,13}
%e A327900   249: {2,23}
%e A327900   255: {2,3,7}
%e A327900   295: {3,17}
%t A327900 Select[Range[1000],!PrimeQ[#]&&SquareFreeQ[#]&&SameQ@@PrimeOmega/@PrimePi/@First/@FactorInteger[#]&]
%Y A327900 The case including primes and nonsquarefree numbers is A320324.
%Y A327900 The version for sum of prime indices is A327901.
%Y A327900 The version for mean of prime indices is A327902.
%Y A327900 Cf. A001222, A038041, A056239, A078175, A112798, A306017, A306021, A316413, A317583, A322794, A327908.
%K A327900 nonn
%O A327900 1,2
%A A327900 _Gus Wiseman_, Sep 30 2019