OFFSET
1,8
COMMENTS
If n is odd, then a(n) = 0 unless n is in A000466, in which case a(n) = 1.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{d|n} c(n/d-d), where c is the prime characteristic (A010051). - Wesley Ivan Hurt, Jan 18 2021
EXAMPLE
a(8) = 2; among the divisors {1,2,4,8} of 8, there are two cases where 8/d-d is prime: 8/1-1 = 7 and 8/2-2 = 2.
MAPLE
f:= proc(n) local D, i, m;
D:= sort(convert(numtheory:-divisors(n), list));
m:= nops(D);
nops(select(i -> isprime(D[m+1-i]-D[i]), [$1..(m+1)/2]));
end proc:
map(f, [$1..100]);
PROG
(PARI) a(n) = sumdiv(n, d, isprime(n/d-d)); \\ Michel Marcus, Jan 18 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Jan 17 2021
STATUS
approved