A325959 a(n) = n - A325967(n).

1, 2, 3, 4, 5, 1, 7, 8, 9, 9, 11, 11, 13, 13, 11, 16, 17, 17, 19, 19, 21, 21, 23, 23, 25, 23, 27, 1, 29, 29, 31, 32, 29, 33, 35, 36, 37, 37, 39, 39, 41, 41, 43, 43, 41, 43, 47, 47, 49, 50, 47, 49, 53, 53, 55, 55, 57, 57, 59, 59, 61, 61, 63, 64, 65, 65, 67, 67, 65, 69, 71, 71, 73, 73, 75, 73, 77, 77, 79, 79, 81, 81, 83, 83, 85, 83, 83

Offset: 1

Author

Antti Karttunen, Jun 01 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..25000
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A325967, A325968, A325969, A325976.

Programs

PARI

A325967aux(n, ds, s, ms, divs, from=1) = if(1==gcd((s-ds)-n,n-ds), return(ds), for(i=from, #divs, if(ds+divs[i] >= ms, return(ms), ms = min(ms,A325967aux(n, ds+divs[i], s, ms, divs, i+1)))); (ms));
A325967(n) = if(1==gcd(n, sigma(n)), 0, my(divs = List(divisors(n)), s=sigma(n), ms=2*s); fordiv(n,d, if(d>=ms, return(ms), listpop(divs,1); ms = min(ms,A325967aux(n, d, s, ms, divs)))); (ms));
A325959(n) = (n - A325967(n));

Formula

a(n) = n - A325967(n).

a(n) = A033879(n) + A325969(n).

For all n, a(n) <= A325976(n).