A330669 The prime indices of the prime powers (A000961).

0, 1, 2, 1, 3, 4, 1, 2, 5, 6, 1, 7, 8, 9, 3, 2, 10, 11, 1, 12, 13, 14, 15, 4, 16, 17, 18, 1, 19, 20, 21, 22, 2, 23, 24, 25, 26, 27, 28, 29, 30, 5, 3, 31, 1, 32, 33, 34, 35, 36, 37, 38, 39, 6, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49

Offset

1,3

Links

Table of n, a(n) for n=1..64.

Formula

a(n) = A000720(A025473(n)). - Michel Marcus, Dec 24 2019

A000040(a(n))^A025474(n) = A000961(n) for n > 0. - Alois P. Heinz, Feb 20 2020

Example

a(16) is 2 since A000961(16) is 27 which is 3^3 = (p_2)^3, i.e., the prime index of 3 is 2.

Maple

b:= proc(n) option remember; local k; for k from
      1+b(n-1) while nops(ifactors(k)[2])>1 do od; k
    end: b(1):=1:
a:= n-> `if`(n=1, 0, numtheory[pi](ifactors(b(n))[2, 1$2])):
seq(a(n), n=1..100);  # Alois P. Heinz, Feb 20 2020

Mathematica

mxn = 500; Join[{0}, Transpose[ Sort@ Flatten[ Table[ {Prime@n^ex, n}, {n, PrimePi@ mxn}, {ex, Log[Prime@n, mxn]}], 1]][[2]]]

Prog

(PARI) lista(nn) = {print1(0); for(n=2, nn, if(isprimepower(n, &p), print1(", ", primepi(p)))); } \\ Jinyuan Wang, Feb 19 2020

Crossrefs

Cf. A000040, A000961, A000720, A025473, A025474, A065515.

Sequence in context: A347354 A361429 A345290 * A084579 A276237 A059663

Adjacent sequences: A330666 A330667 A330668 * A330670 A330671 A330672

Keyword

easy,nonn

Author

Grant E. Martin and Robert G. Wilson v, Dec 23 2019

Status

approved