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A325818
a(n) is the largest k <= sigma(n) such that n-k and n-(sigma(n)-k) are relatively prime.
11
1, 3, 4, 7, 6, 7, 8, 15, 13, 17, 12, 27, 14, 23, 22, 31, 18, 38, 20, 41, 32, 35, 24, 59, 31, 39, 40, 29, 30, 71, 32, 63, 46, 53, 48, 91, 38, 59, 56, 89, 42, 95, 44, 83, 76, 69, 48, 123, 57, 93, 70, 95, 54, 119, 72, 119, 80, 89, 60, 167, 62, 95, 104, 127, 84, 143, 68, 125, 94, 143, 72, 194, 74, 113, 124, 137, 96
OFFSET
1,2
COMMENTS
a(n) is the largest k <= sigma(n) such that (-n + k) and (n-sigma(n))+k are coprime.
FORMULA
a(n) = A000203(n) - A325817(n).
a(n) = n + A325826(n).
For all n:
a(A000396(n)) = A000396(n)+1.
a(n) >= A325961(n).
a(n) >= A325966(n).
a(n) >= A325968(n).
PROG
(PARI) A325818(n) = { my(s=sigma(n)); for(i=0, s, if(1==gcd(n-i, n-(s-i)), return(s-i))); };
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 29 2019
STATUS
approved