A216982 Anti-Chowla's function: sum of anti-divisors of n except the largest.

0, 0, 0, 0, 2, 0, 5, 3, 2, 7, 5, 5, 10, 7, 8, 3, 17, 16, 5, 11, 8, 21, 19, 7, 22, 7, 24, 27, 5, 16, 21, 37, 26, 7, 29, 8, 25, 45, 26, 28, 14, 38, 27, 11, 56, 27, 29, 24, 39, 47, 8, 59, 53, 16, 37, 19, 36, 57, 51, 67, 16, 37, 70, 3, 41, 42, 87, 67, 8, 55

Offset

1,5

Comments

Numbers n such that Chowla's function(n) = a(n): 1, 2, 3, 10, 15, 28, 75, 88, 231, 284, 602,...

Places n where a(n) is zero: 1, 2, 3, 4, 6, 96,...

Fixed points of this sequence: 17, 53, 127, 217, 385, 2321,...

Places n where a(n) equals the largest anti-divisor: 1, 2, 7, 10, 31, 37, 39, 55, 78, 160, 482, 937, 1599, 2496,...

Numbers n such that n -/+ 1 and a(n -/+ 1) are all primes: 6, 18, 72, 102, 108, 198, 270, 432, 570, 882,...

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) = A066417(n) - A066481(n).

Example

Anti-divisors of 7 are 2, 3, 5, so a(7) = 2 + 3 = 5.

Maple

A216982 := proc(n)
        A066417(n)-A066481(n) ;
end proc: # R. J. Mathar, Feb 23 2013

Prog

(PARI) a(n)=if(n<5, 0, my(k=valuation(n, 2)); sigma(2*n+1)+sigma(2*n-1)+sigma(n>>k)<<(k+1)-2-20*n\/3) \\ Charles R Greathouse IV, Mar 05 2013

Crossrefs

Cf. A048050, A066272, A066417, A066481, A130799, A218767.

Sequence in context: A132816 A261068 A077453 * A184854 A021491 A324654

Adjacent sequences: A216979 A216980 A216981 * A216983 A216984 A216985

Keyword

nonn

Author

Juri-Stepan Gerasimov, Feb 19 2013

Status

approved