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A216982 Anti-Chowla's function: sum of anti-divisors of n except the largest. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 26 01:08 EDT 2019. Contains 321479 sequences. (Running on oeis4.)