A369558 - OEIS

%I #10 Mar 17 2024 04:01:37

%S 2,6,4,1,6,3,7,5,10,110,6,9,13,1,10,193,6,15,1,9,22,250,1,10,6,1,5,

%T 370,8,27,7,23,34,1,6,398,2,6,9,610,4,39,13,7,2,730,6,1,1,9,3,850,11,

%U 9,6,28,58,1586,3,57,8,13,2,7,3,818,25,5,11,1210,5,69,1,11

%N a(n) is the minimum value of k > 0 such that A075860(n) = A075860(n+k) with n > 1.

%e For n=5, A075860(5) = A075860(5+1), so a(5)=1.

%e For n=15, A075860(15) = A075860(15+1), so a(15)=1.

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

%p     if isprime(n) then

%p         n;

%p     else

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

%p     fi;

%p end proc:

%p g := proc(n)

%p     local k;

%p     for k from 1 do

%p         if f(n+k) = f(n) then

%p             return k;

%p         fi;

%p     end do;

%p end proc:

%p map(g, [$2..100]);

%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));

%o a(n) = my(k=1, fn=f(n)); while(f(n+k) != fn, k++); k; \\ _Michel Marcus_, Feb 20 2024

%Y Cf. A075860.

%K nonn

%O 2,1

%A _Rafik Khalfi_, Jan 25 2024