A309219 Number of distinct primes formed by concatenating two (not necessarily distinct) divisors of n.

1, 1, 3, 2, 1, 5, 3, 2, 4, 2, 1, 7, 3, 3, 5, 2, 1, 8, 2, 3, 8, 2, 1, 9, 2, 3, 6, 6, 1, 9, 3, 2, 6, 1, 3, 10, 2, 2, 7, 4, 1, 12, 2, 3, 7, 3, 1, 10, 5, 3, 6, 5, 1, 12, 1, 6, 7, 2, 1, 12, 1, 3, 13, 3, 3, 12, 2, 2, 5, 6, 1, 13, 2, 2, 7, 5, 3, 12, 2, 4, 8, 3, 1, 18

Offset

1,3

Comments

If a prime arises in more than one way it is only counted once (in contrast to A309460).

Links

Marius A. Burtea, Table of n, a(n) for n = 1..5000

Example

For n = 1,2,3,4,... the primes are:
1: 11;
2: 11;
3: 11,13,31;
4: 11,41;
5: 11;
6: 11,13,23,31,61;
7: 11,17,71;
...

Maple

a:= n-> (l-> nops(select(isprime, {seq(seq(parse(
        cat(i, j)), j=l), i=l)})))(numtheory[divisors](n)):
seq(a(n), n=1..100);  # Alois P. Heinz, Aug 13 2019

Prog

(Magma) m:=1; sol:=[]; for u in [1..84] do d:=Divisors(u); nr:=0; prim:=[]; for i, j in [1..#d] do if IsPrime(d[i]*10^#Intseq(d[j])+d[j]) then nr:=nr+1; prim[nr]:=d[i]*10^#Intseq(d[j])+d[j]; end if; end for; sol[m]:=#Set(prim);  m:=m+1; end for; sol; // Marius A. Burtea, Aug 12 2019

Crossrefs

Cf. A000005, A309460.

Sequence in context: A171746 A113977 A183162 * A019587 A102427 A080883

Adjacent sequences: A309216 A309217 A309218 * A309220 A309221 A309222

Keyword

nonn,base

Author

N. J. A. Sloane, Aug 12 2019

Status

approved