A039736 a(n) = number of primes q<p having (p mod q) = 2, where p = n-th prime.

0, 0, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 3, 2, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 2, 1, 2, 3, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 3, 2, 2, 3, 1, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 1, 3, 1, 2, 2, 2, 3, 2, 1, 3, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 3, 3, 2, 1

Offset

1,7

Comments

Number of distinct prime factors of prime(n) - 2.

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Example

First prime is 2, p_1-2 = 0 which has no prime factors, 2nd is 3, 3-2 = 1 which also has no prime factors. p_6 is 17 and 15 has 2 distinct prime divisors. a(219) = A001221(Prime(219)-2) = A001221(1365) = A001221(3*5*7*13) = 4

Mathematica

Table[Length[FactorInteger[Prime[n]-2]], {n, 1, 50}]
Join[{0}, Table[PrimeNu[Prime[n] - 2], {n, 2, 50}]] (* G. C. Greubel, May 19 2017 *)

Prog

(PARI) concat([0], for(n=2, 50, print1(omega(prime(n) - 2), ", "))) \\ G. C. Greubel, May 19 2017

Crossrefs

Cf. A001221.

Sequence in context: A237442 A277070 A139355 * A093921 A353426 A140192

Adjacent sequences: A039733 A039734 A039735 * A039737 A039738 A039739

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Labos Elemer

Status

approved