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A325976
a(n) is the largest k <= n such that k and (2n-sigma(n)) [= A033879(n)] are relatively prime.
5
1, 2, 3, 4, 5, 1, 7, 8, 9, 9, 11, 11, 13, 13, 13, 16, 17, 17, 19, 19, 21, 21, 23, 23, 25, 23, 27, 1, 29, 29, 31, 32, 31, 33, 35, 36, 37, 37, 39, 39, 41, 41, 43, 43, 43, 43, 47, 47, 49, 50, 49, 49, 53, 53, 55, 55, 57, 57, 59, 59, 61, 61, 63, 64, 65, 65, 67, 67, 67, 69, 71, 71, 73, 73, 75, 73, 77, 77, 79, 79, 81, 81, 83, 83, 85, 83
OFFSET
1,2
FORMULA
a(n) = n - A325817(n) = A033879(n) + A325826(n).
a(n) >= A325959(n).
gcd(a(n), A325826(n)) = 1.
PROG
(PARI) A325976(n) = { my(s=sigma(n)); forstep(k=n, 0, -1, if(1==gcd((n+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))); };
A325976(n) = (n - A325817(n));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 01 2019
STATUS
approved