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A325961
a(n) is the least k >= A061228(n)-1 such that n-k and n-(sigma(n)-k) are relatively prime, or 0 if no such k <= sigma(n) exists.
8
1, 3, 0, 5, 0, 7, 0, 9, 11, 11, 0, 13, 0, 15, 20, 17, 0, 19, 0, 21, 24, 23, 0, 25, 29, 27, 30, 29, 0, 31, 0, 33, 38, 35, 40, 37, 0, 39, 42, 41, 0, 43, 0, 45, 50, 47, 0, 49, 55, 51, 58, 53, 0, 55, 60, 57, 60, 59, 0, 61, 0, 63, 66, 65, 70, 67, 0, 69, 74, 71, 0, 73, 0, 75, 78, 77, 84, 79, 0, 81, 83, 83, 0, 85, 90, 87, 92, 89, 0, 91, 100
OFFSET
1,2
COMMENTS
a(n) attains the value of A325818(n) only with n = 1, 2 and the even terms of A000396. Note that A000203(n) > ((n+A020639(n))-1) with composite n.
FORMULA
a(n) = 0 if and only if n is either an odd prime or an odd perfect number, but if n is neither, then a(n) = 2n - A325962(n).
PROG
(PARI)
A020639(n) = if(1==n, n, factor(n)[1, 1]);
A325961(n) = { my(s=sigma(n)); for(i=(-1)+n+A020639(n), s, if(1==gcd(n-i, n-(s-i)), return(i))); (0); };
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 29 2019
STATUS
approved