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A369558 a(n) is the minimum value of k > 0 such that A075860(n) = A075860(n+k) with n > 1.

%I A369558 #10 Mar 17 2024 04:01:37
%S A369558 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 A369558 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 A369558 9,6,28,58,1586,3,57,8,13,2,7,3,818,25,5,11,1210,5,69,1,11
%N A369558 a(n) is the minimum value of k > 0 such that A075860(n) = A075860(n+k) with n > 1.
%e A369558 For n=5, A075860(5) = A075860(5+1), so a(5)=1.
%e A369558 For n=15, A075860(15) = A075860(15+1), so a(15)=1.
%p A369558 f := proc(n) option remember;
%p A369558     if isprime(n) then
%p A369558         n;
%p A369558     else
%p A369558         procname(convert(numtheory:-factorset(n), `+`));
%p A369558     fi;
%p A369558 end proc:
%p A369558 g := proc(n)
%p A369558     local k;
%p A369558     for k from 1 do
%p A369558         if f(n+k) = f(n) then
%p A369558             return k;
%p A369558         fi;
%p A369558     end do;
%p A369558 end proc:
%p A369558 map(g, [$2..100]);
%o A369558 (PARI) fp(n, pn) = if (n == pn, n, fp(vecsum(factor(n)[, 1]), n));
%o A369558 f(n) = if (n==1, 0, fp(n, 0));
%o A369558 a(n) = my(k=1, fn=f(n)); while(f(n+k) != fn, k++); k; \\ _Michel Marcus_, Feb 20 2024
%Y A369558 Cf. A075860.
%K A369558 nonn
%O A369558 2,1
%A A369558 _Rafik Khalfi_, Jan 25 2024