A327900 - OEIS

%I #5 Oct 01 2019 09:48:42

%S 1,15,33,51,55,85,91,93,123,155,161,165,177,187,201,203,205,249,255,

%T 295,299,301,327,329,335,341,377,381,415,451,465,471,511,527,537,545,

%U 553,559,561,573,611,615,633,635,649,667,679,697,703,707,723,737,785,831

%N Nonprime squarefree numbers whose prime indices all have the same Omega (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.

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

%e     1: {}

%e    15: {2,3}

%e    33: {2,5}

%e    51: {2,7}

%e    55: {3,5}

%e    85: {3,7}

%e    91: {4,6}

%e    93: {2,11}

%e   123: {2,13}

%e   155: {3,11}

%e   161: {4,9}

%e   165: {2,3,5}

%e   177: {2,17}

%e   187: {5,7}

%e   201: {2,19}

%e   203: {4,10}

%e   205: {3,13}

%e   249: {2,23}

%e   255: {2,3,7}

%e   295: {3,17}

%t Select[Range[1000],!PrimeQ[#]&&SquareFreeQ[#]&&SameQ@@PrimeOmega/@PrimePi/@First/@FactorInteger[#]&]

%Y The case including primes and nonsquarefree numbers is A320324.

%Y The version for sum of prime indices is A327901.

%Y The version for mean of prime indices is A327902.

%Y Cf. A001222, A038041, A056239, A078175, A112798, A306017, A306021, A316413, A317583, A322794, A327908.

%K nonn

%O 1,2

%A _Gus Wiseman_, Sep 30 2019