A325960 - OEIS

%I #10 Jun 02 2019 00:51:34

%S 0,1,0,1,0,1,0,1,2,1,0,1,0,1,5,1,0,1,0,1,3,1,0,1,4,1,3,1,0,1,0,1,5,1,

%T 5,1,0,1,3,1,0,1,0,1,5,1,0,1,6,1,7,1,0,1,5,1,3,1,0,1,0,1,3,1,5,1,0,1,

%U 5,1,0,1,0,1,3,1,7,1,0,1,2,1,0,1,5,1,5,1,0,1,9,1,3,1,9,1,0,1,5,1,0,1,0,1,5

%N a(n) is k-n for the least k >= n+(A020639(n)-1) such that n-k and n-(sigma(n)-k) are relatively prime, or 0 if no such k <= sigma(n) exists.

%C By definition, if n is neither an odd prime nor an odd perfect number, then a(n) >= (A020639(n)-1).

%H Antti Karttunen, <a href="/A325960/b325960.txt">Table of n, a(n) for n = 1..65537</a>

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

%F a(n) = (A325961(n) - A325962(n)) / 2, assuming no odd perfect numbers exist.

%F a(2n) = 1.

%o (PARI)

%o A020639(n) = if(1==n, n, factor(n)[1, 1]);

%o A325960(n) = { my(s=sigma(n)); for(i=(-1)+n+A020639(n), s, if(1==gcd(n-i, n-(s-i)), return(i-n))); (0); };

%Y Cf. A000203, A000396, A020639, A324213, A325817, A325818, A325826, A325961, A325962, A325965, A325966, A325970.

%Y Cf. A006005 (positions of zeros, provided no odd perfect numbers exist).

%K nonn

%O 1,9

%A _Antti Karttunen_, May 29 2019