A328948 Number of primes that are a concatenation of two positive integers whose product is n.

1, 0, 2, 1, 0, 2, 2, 0, 1, 1, 0, 1, 2, 0, 2, 0, 0, 2, 1, 0, 3, 1, 0, 2, 1, 0, 2, 2, 0, 1, 2, 0, 3, 0, 0, 0, 1, 0, 2, 1, 0, 2, 1, 0, 1, 2, 0, 1, 2, 0, 3, 1, 0, 2, 0, 0, 3, 1, 0, 1, 0, 0, 4, 1, 0, 3, 1, 0, 2, 2, 0, 1, 1, 0, 1, 2, 0, 3, 1, 0, 2, 2, 0, 3, 0, 0, 1, 2, 0, 1, 3, 0, 3, 1, 0, 0

Offset

1,3

Comments

Records: 1, 3, 21, 63, 231, 924, 4389, 5187, 51051, 69069, 127281, 245973, 302841, 969969, 1312311, 1716099. - Corrected by Robert Israel, Dec 14 2023

This is not always the same as the number of divisors d of n such that the concatenation of d and n/d is prime, because the same prime could occur for more than one divisor. For example, 1140678 = 14*81477 = 14814*77 with 1481477 prime, and this prime is counted only once in a(1140678) = 7. - Robert Israel, Dec 14 2023

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(3n + 2) = 0.

Example

1(11), 2(-), 3(13, 31), 4(41), 5(-), 6(23, 61), 7(17, 71), 8(-), 9(19), 10(101), 11(-), 12(43), 13(113, 131), 14(-), 15(53, 151), 16(-).

Maple

f:= proc(n)
   if n mod 3 = 2 then return 0 fi;
   nops(select(isprime, {seq(dcat(t, n/t), t = numtheory:-divisors(n))})
end proc:
map(f, [$1..200]); # Robert Israel, Dec 14 2023

Prog

(PARI) a(n) = sumdiv(n, d, isprime(eval(concat(Str(d), Str(n/d))))); \\ Michel Marcus, Nov 05 2019
(Magma) [#[a: d in Divisors(n)| IsPrime(a) where a is Seqint(Intseq(d) cat Intseq(n div d))]:n in [1..100]]; // Marius A. Burtea, Nov 05 2019

Crossrefs

Cf. A000040, A016789, A161904, A328903.

Sequence in context: A258279 A258292 A003985 * A287524 A157237 A065676

Adjacent sequences: A328945 A328946 A328947 * A328949 A328950 A328951

Keyword

nonn,base,easy

Author

Juri-Stepan Gerasimov, Nov 01 2019

Status

approved