A023510 Greatest exponent in prime-power factorization of prime(n) + 1.

1, 2, 1, 3, 2, 1, 2, 2, 3, 1, 5, 1, 1, 2, 4, 3, 2, 1, 2, 3, 1, 4, 2, 2, 2, 1, 3, 3, 1, 1, 7, 2, 1, 2, 2, 3, 1, 2, 3, 1, 2, 1, 6, 1, 2, 3, 2, 5, 2, 1, 2, 4, 2, 2, 1, 3, 3, 4, 1, 1, 2, 2, 2, 3, 1, 1, 2, 2, 2, 2, 1, 3, 4, 1, 2, 7, 1, 1, 1, 1, 2, 1, 4, 1, 3, 2, 2, 1, 1, 4, 2, 5, 3, 2, 3, 3, 1, 2, 2

Offset

1,2

Comments

If a(n)=1 then prime(a(n)) is a term in A049097. - Zak Seidov, Jul 20 2016

Links

Zak Seidov, Table of n, a(n) for n = 1..10000

Formula

a(n) = A051903(A008864(n)). - Michel Marcus, Jul 20 2016

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A392818. - Amiram Eldar, Jan 24 2026

Example

For n=5, the fifth prime is 11, and the prime factorization of 11 + 1 = 12 is 2^2*3. This has exponents 2 and 1, so a(5) is the largest of these exponents, 2. - Michael B. Porter, Jul 20 2016

Mathematica

Table[Max[#[[2]] & /@ FactorInteger[Prime[k] + 1]], {k, 10000}] (* Zak Seidov, Jul 19 2016 *)

Prog

(PARI) a(n) = vecmax(factor(prime(n)+1)[, 2]) \\ Michel Marcus, Jul 20 2016

Crossrefs

Cf. A008864, A023504, A023509, A049097, A051903, A392818.

Sequence in context: A374740 A153359 A240474 * A005678 A296976 A182321

Adjacent sequences: A023507 A023508 A023509 * A023511 A023512 A023513

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved