cp's OEIS Frontend

A360615 Denominator of the average distance between consecutive 0-prepended prime indices of n; a(1) = 0.

%I A360615 #14 Feb 20 2023 12:25:50
%S A360615 0,1,1,2,1,1,1,3,1,2,1,3,1,1,2,4,1,3,1,1,1,2,1,2,2,1,3,3,1,1,1,5,2,2,
%T A360615 1,2,1,1,1,4,1,3,1,3,1,2,1,5,1,1,2,1,1,2,2,1,1,1,1,4,1,2,3,6,1,3,1,3,
%U A360615 2,3,1,5,1,1,1,3,2,1,1,5,2,2,1,1,2,1,1,4
%N A360615 Denominator of the average distance between consecutive 0-prepended prime indices of n; a(1) = 0.
%C A360615 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 A360615 Winston de Greef, <a href="/A360615/b360615.txt">Table of n, a(n) for n = 1..10000</a>
%F A360615 Denominator of A061395(n)/A001222(n), for n>1.
%e A360615 The 0-prepended prime indices of 100 are {0,1,1,3,3}, with differences (1,0,2,0), with mean 3/4, so a(100) = 4.
%t A360615 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A360615 Table[If[n==1,0,Denominator[Mean[Differences[Prepend[prix[n],0]]]]],{n,100}]
%o A360615 (PARI) a(n) = if (n==1, 0, my(f=factor(n)); denominator(primepi(vecmax(f[, 1]))/ bigomega(f))); \\ _Michel Marcus_, Feb 20 2023
%Y A360615 Positions of 1's are A340610
%Y A360615 The numerator is A360614.
%Y A360615 A112798 lists prime indices, length A001222, sum A056239, max A061395.
%Y A360615 A124010 gives prime signature, mean A088529/A088530.
%Y A360615 A316413 lists numbers with integer mean prime index, complement A348551.
%Y A360615 A326567/A326568 gives mean of prime indices.
%Y A360615 Cf. A106529, A334201, A340609, A360008, A360555, A360556, A360558.
%K A360615 nonn,frac
%O A360615 1,4
%A A360615 _Gus Wiseman_, Feb 19 2023