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A360615
Denominator of the average distance between consecutive 0-prepended prime indices of n; a(1) = 0.
11
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, 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, 2, 3, 1, 5, 1, 1, 1, 3, 2, 1, 1, 5, 2, 2, 1, 1, 2, 1, 1, 4
OFFSET
1,4
COMMENTS
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.
LINKS
FORMULA
Denominator of A061395(n)/A001222(n), for n>1.
EXAMPLE
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.
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[If[n==1, 0, Denominator[Mean[Differences[Prepend[prix[n], 0]]]]], {n, 100}]
PROG
(PARI) a(n) = if (n==1, 0, my(f=factor(n)); denominator(primepi(vecmax(f[, 1]))/ bigomega(f))); \\ Michel Marcus, Feb 20 2023
CROSSREFS
Positions of 1's are A340610
The numerator is A360614.
A112798 lists prime indices, length A001222, sum A056239, max A061395.
A124010 gives prime signature, mean A088529/A088530.
A316413 lists numbers with integer mean prime index, complement A348551.
A326567/A326568 gives mean of prime indices.
Sequence in context: A316557 A353381 A032436 * A280274 A073408 A372572
KEYWORD
nonn,frac
AUTHOR
Gus Wiseman, Feb 19 2023
STATUS
approved