A359249 - OEIS

A359249

a(n) is the number of primes p such that (n/p)^2 + 1 is prime.

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

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OFFSET

1,12

LINKS

Table of n, a(n) for n=1..100.

EXAMPLE

a(12) = 2 because 12 = 2*6 (p = 2 and q = 6^2 + 1 = 37) and 12 = 3*4 (p = 3 and q = 4^2 + 1 = 17).

PROG

(Magma) [#[p: p in [1..n] | n mod p eq 0 and IsPrime(p) and IsPrime((n^2 div p^2) + 1)]: n in [1..100]];

(PARI) a(n) = sumdiv(n, p, isprime(p) && isprime((n/p)^2+1)); \\ Michel Marcus, Dec 23 2022

CROSSREFS

Cf. A002496, A005574.

Sequence in context: A016388 A016004 A327802 * A284996 A215029 A362832

Adjacent sequences: A359246 A359247 A359248 * A359250 A359251 A359252

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Dec 22 2022

STATUS

approved

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