A374330 a(n) is the number of numbers k <= prime(n)^2 such that A075860(k) = prime(n).

2, 2, 6, 8, 2, 10, 3, 14, 6, 8, 22, 7, 8, 21, 9, 14, 12, 45, 14, 17, 45, 17, 21, 20, 18, 17, 64, 21, 54, 28, 25, 22, 22, 72, 37, 82, 26, 28, 31, 43, 36, 93, 44, 95, 38, 95, 41, 38, 33, 106, 36, 49, 111, 65, 53, 53, 49, 113, 55, 68, 138, 80, 49, 50, 152, 61, 55, 43, 73, 120

Offset: 1

Author

Rafik Khalfi, Jul 04 2024

Keywords

• nonn

Comments

For all n>=1, a(n)>=2.

Examples

			For n=3, prime(3)=5. The only integers k <= 5^2 such that A075860(k)=5 are 5,6,12,18,24 and 25. Therefore a(3)=6.
		

Crossrefs

Cf. A001248, A075860.

Programs

Maple

f := proc (n)
    option remember;
    if isprime(n) then
        return n
    else
        return procname(convert(numtheory:-factorset(n), `+`))
    end if
end proc:
g := proc (n)
    local count, k;
    count := 0;
    for k from ithprime(n) to ithprime(n)^2 do
        if f(k) = ithprime(n) then
            count := count + 1
        end if
    end do;
    return count
end proc:
map(g, [$1 .. 80]);

PARI

fp(n, pn) = if (n == pn, n, fp(vecsum(factor(n)[, 1]), n));
f(n) = if (n==1, 0, fp(n, 0)); \\ A075860
a(n) = sum(k=1, prime(n)^2, f(k) == prime(n)); \\ Michel Marcus, Jul 04 2024