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

Author

Juri-Stepan Gerasimov, Nov 01 2019

Keywords

• nonn
• base
• easy

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

Examples

			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(-).
		

Links

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

Crossrefs

Cf. A000040, A016789, A161904, A328903.

Programs

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

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

PARI

a(n) = sumdiv(n, d, isprime(eval(concat(Str(d), Str(n/d))))); \\ Michel Marcus, Nov 05 2019

Formula

a(3n + 2) = 0.