cp's OEIS Frontend

A379300 Number of prime indices of n that are composite.

%I A379300 #13 Dec 26 2024 21:43:33
%S A379300 0,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,1,0,1,0,1,0,0,1,0,1,1,0,0,0,0,0,
%T A379300 1,0,1,1,1,0,0,1,1,0,0,1,1,0,2,0,0,1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,0,
%U A379300 1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,1
%N A379300 Number of prime indices of n that are composite.
%C A379300 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.
%F A379300 Totally additive with a(prime(k)) = A066247(k).
%e A379300 The prime indices of 39 are {2,6}, so a(39) = 1.
%e A379300 The prime indices of 70 are {1,3,4}, so a(70) = 1.
%e A379300 The prime indices of 98 are {1,4,4}, so a(98) = 2.
%e A379300 The prime indices of 294 are {1,2,4,4}, a(294) = 2.
%e A379300 The prime indices of 1911 are {2,4,4,6}, so a(1911) = 3.
%e A379300 The prime indices of 2548 are {1,1,4,4,6}, so a(2548) = 3.
%t A379300 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A379300 Table[Length[Select[prix[n],CompositeQ]],{n,100}]
%Y A379300 Positions of first appearances are A000420.
%Y A379300 Positions of zero are A302540, counted by A034891 (strict A036497).
%Y A379300 Positions of one are A379301, counted by A379302 (strict A379303).
%Y A379300 A000040 lists the prime numbers, differences A001223.
%Y A379300 A002808 lists the composite numbers, nonprimes A018252, differences A073783 or A065310.
%Y A379300 A055396 gives least prime index, greatest A061395.
%Y A379300 A056239 adds up prime indices, row sums of A112798, counted by A001222.
%Y A379300 A066247 is the characteristic function for the composite numbers.
%Y A379300 A377033 gives k-th differences of composite numbers, see A073445, A377034-A377037.
%Y A379300 Other counts of prime indices:
%Y A379300 - A087436 postpositive, see A038550.
%Y A379300 - A257991 odd, see A000041, A000070, A066207, A349158.
%Y A379300 - A257992 even, see A000009, A038348, A066208, A379317.
%Y A379300 - A257994 prime, see A000586, A000607, A076610, A331386, A331915, A379304, A379305.
%Y A379300 - A330944 nonprime, see A002095, A096258, A320628, A330945.
%Y A379300 - A379306 squarefree, see A302478, A379308, A379309, A379316.
%Y A379300 - A379310 nonsquarefree, see A114374, A256012, A379307.
%Y A379300 - A379311 old prime, see A379312-A379315.
%Y A379300 Cf. A023895, A113646, A175804, A204389, A320629, A376680, A378373, A378456.
%K A379300 nonn
%O A379300 1,49
%A A379300 _Gus Wiseman_, Dec 25 2024