A325970 - OEIS

%I #11 Jun 02 2019 00:52:14

%S 0,0,-1,2,-1,-1,-1,6,6,-1,-1,5,-1,-1,-1,14,-1,11,-1,9,-1,-1,-1,17,20,

%T -1,23,1,-1,-1,-1,30,-1,-1,-1,30,-1,-1,-1,29,-1,-1,-1,21,29,-1,-1,41,

%U 42,40,-1,25,-1,47,-1,41,-1,-1,-1,29,-1,-1,41,62,-1,-1,-1,33,-1,-1,-1,65,-1,-1,59,37,-1,-1,-1,69,78

%N a(n) is the largest k <= A066503(n) such that k and (2n-sigma(n)) [= A033879(n)] are relatively prime.

%C a(n) = n-k for the least k >= A007947(n) such that n-k and n-(sigma(n)-k) are relatively prime.

%H Antti Karttunen, <a href="/A325970/b325970.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A325970/a325970.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = n - A325971(n).

%F For n >= 3, a(A005117(n)) = -1.

%o (PARI)

%o A007947(n) = factorback(factorint(n)[, 1]); \\ From A007947

%o A325970(n) = { my(s=sigma(n)); forstep(k=n-A007947(n), -oo, -1, if(1==gcd(k, n+n-sigma(n)), return(k))); };

%o \\ Or alternatively:

%o A325970(n) = { my(s=sigma(n)); for(i=A007947(n), s, if(1==gcd(n-i, n-(s-i)), return(n-i))); };

%Y Cf. A000203, A005117, A007947, A033879, A066503, A324213, A325826, A325960, A325967, A325971, A325972.

%K sign

%O 1,4

%A _Antti Karttunen_, May 31 2019