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A325817
a(n) is the least k >= 0 such that n-k and n-(sigma(n)-k) are relatively prime.
11
0, 0, 0, 0, 0, 5, 0, 0, 0, 1, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 3, 0, 27, 0, 1, 0, 0, 2, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 2, 3, 0, 1, 0, 0, 2, 3, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 1, 0, 1, 0, 3, 2, 1, 0, 1, 2, 1, 0, 1, 2, 5, 0, 0, 2, 0, 0, 1, 0, 1, 2
OFFSET
1,6
COMMENTS
a(n) is the least k >= 0 such that -n + k and (n-sigma(n))+k are coprime.
FORMULA
a(n) = A000203(n) - A325818(n) = A001065(n) - A325826(n) = n - A325976(n).
For all n:
a(A000396(n)) = A000396(n)-1.
a(n) <= n-1.
a(n) <= A325965(n).
a(n) <= A325967(n).
EXAMPLE
For n=15, gcd(15-0, 15-(24-0)) = 3, gcd(15-1, 15-(24-1)) = 2 and gcd(15-2, 15-(24-2)) = 1, thus a(15) = 2.
PROG
(PARI) A325817(n) = { my(s=sigma(n)); for(k=0, s, if(1==gcd(-n + k, (n-s)+k), return(k))); };
(PARI) A325817(n) = { my(s=sigma(n)); for(i=0, s, if(1==gcd(n-i, n-(s-i)), return(i))); };
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 29 2019
STATUS
approved