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a(n) = A075860(A075860(n) + 2) + 2.
0

%I #17 Jul 23 2024 21:40:19

%S 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,

%T 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,

%U 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

%N a(n) = A075860(A075860(n) + 2) + 2.

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

%C For all positive integers n, there exists a positive integer m such that a(n)<a(m).

%p g:= proc(n) option remember;

%p if isprime(n) then n

%p else procname(convert(numtheory:-factorset(n), `+`))

%p fi

%p end proc:

%p g(1):= 0:

%p seq(2+g(2+g(i)),i=1..140);

%o (PARI) fp(n, pn) = if (n == pn, n, fp(vecsum(factor(n)[, 1]), n));

%o f(n) = if (n==1, 0, fp(n, 0)); \\ A075860

%o a(n) = f(f(n)+2)+2; \\ _Michel Marcus_, Jun 28 2024

%Y Cf. A075860, A008472.

%K nonn

%O 1,1

%A _Rafik Khalfi_, Jun 28 2024