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A325966
a(n) is the largest i <= sigma(n)-A020639(n) such that n-i and n-(sigma(n)-i) are relatively prime.
8
0, 1, 0, 5, 0, 7, 0, 13, 10, 15, 0, 25, 0, 21, 20, 29, 0, 37, 0, 39, 28, 33, 0, 55, 26, 39, 36, 29, 0, 67, 0, 61, 44, 51, 42, 89, 0, 57, 52, 87, 0, 91, 0, 81, 74, 69, 0, 121, 50, 91, 68, 95, 0, 115, 66, 117, 76, 87, 0, 163, 0, 93, 100, 125, 78, 139, 0, 121, 92, 141, 0, 193, 0, 111, 120, 137, 88, 163, 0, 183, 118, 123, 0
OFFSET
1,4
FORMULA
a(n) = A000203(n) - A325965(n).
For all n:
a(A000396(n)) = A000396(n)+1.
a(n) <= A325818(n).
PROG
(PARI)
A020639(n) = if(1==n, n, factor(n)[1, 1]);
A325966(n) = { my(s=sigma(n)); forstep(i=s-A020639(n), 0, -1, if(1==gcd(n-i, n-(s-i)), return(i))); };
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 29 2019
STATUS
approved