A374104 a(n) = A075860(A075860(n) + 2) + 2.

4, 4, 7, 4, 9, 9, 5, 4, 7, 5, 15, 9, 4, 7, 4, 4, 21, 9, 9, 5, 5, 4, 7, 9, 9, 4, 7, 7, 33, 5, 5, 4, 7, 9, 9, 9, 4, 5, 4, 5, 45, 9, 4, 4, 4, 9, 9, 9, 5, 5, 5, 4, 4, 9, 4, 7, 4, 5, 63, 5, 9, 7, 5, 4, 9, 4, 4, 9, 4, 7, 75, 9, 4, 4, 4, 5, 9, 9, 5, 5, 7, 4, 15, 9, 4, 4, 4, 4, 9, 5, 5, 9

Offset: 1

Author

Rafik Khalfi, Jun 28 2024

Keywords

• nonn

Comments

(p,p+2) is a twin prime pair if and only if a(p)=p+4.

For all positive integers n, there exists a positive integer m such that a(n)

Crossrefs

Cf. A075860, A008472.

Programs

Maple

g:= proc(n) option remember;
    if isprime(n) then n
   else procname(convert(numtheory:-factorset(n), `+`))
    fi
 end proc:
 g(1):= 0:
seq(2+g(2+g(i)),i=1..140);

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) = f(f(n)+2)+2; \\ Michel Marcus, Jun 28 2024

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