A072612 Minimal value of { abs(n-sigma(k)) : k>0 }.

0, 1, 0, 0, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 0, 0, 0, 1, 2, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 2, 3, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 3, 2, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1

Offset

1,10

Comments

a(A002191(k)) = 0

Links

Table of n, a(n) for n=1..105.

Formula

Conjecture : S(n) = sum( k=1, n, a(k) ) = n + O(sqrt(n)) and more precisely for n large enough : n - (5/2)*sqrt(n) < S(n) < n - (3/2)*sqrt(n)

Prog

(PARI) a(n)=vecmin(vector(n, k, abs(n-sigma(k))))

Crossrefs

Sequence in context: A049816 A328958 A143542 * A116378 A321854 A227839

Adjacent sequences: A072609 A072610 A072611 * A072613 A072614 A072615

Keyword

easy,nonn

Author

Benoit Cloitre, Aug 11 2002

Status

approved