login
A309219
Number of distinct primes formed by concatenating two (not necessarily distinct) divisors of n.
2
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
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
Sequence in context: A171746 A113977 A183162 * A019587 A102427 A080883
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Aug 12 2019
STATUS
approved