A343240 The number of solutions x from {0, 1, ..., A343238(n)-1} of the congruence x^2 + 5 == 0 (mod A343238(n)) is given by a(n).

1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 4, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 4, 2, 4, 2, 2, 4, 4, 2, 4, 2, 4, 2, 2, 2, 2, 4, 2, 2, 4, 4, 4, 2, 4, 2, 2, 4

Offset

1,3

Comments

Row length of irregular triangle A343239.

Links

Table of n, a(n) for n=1..74.

Formula

a(n) = row length of A343239(n), for n >= 1.

a(1) = a(2) = a(4) = a(8) = 1, and otherwise a(n) = 2^{number of distinct primes from A139513}, that is, primes congruent to {1, 3, 7, 9} (mod 20), appearing in the prime factorization of A343238(n).

Example

a(19) = 4 because A343238(19) = 42 = 2*3*7 has 2^(1+1) = 4 solutions from the primes 3 and 7.

Prog

(PARI) isok(k) = issquare(Mod(-5, k)); \\ A343238
lista(nn) = my(list = List()); for (n=1, nn, if (issquare(Mod(-5, n)), listput(list, sum(i=0, n-1, Mod(i, n)^2 + 5 == 0)); ); ); Vec(list); \\ Michel Marcus, Sep 17 2023

Crossrefs

Cf. A343238, A343239.

Sequence in context: A353929 A297770 A330617 * A145866 A103318 A197775

Adjacent sequences: A343237 A343238 A343239 * A343241 A343242 A343243

Keyword

nonn,easy

Author

Wolfdieter Lang, May 16 2021

Status

approved