A073954 Numbers k such that the sum of the anti-divisors of k exceeds 2*k.

143, 175, 203, 247, 248, 270, 280, 297, 315, 325, 333, 347, 357, 368, 410, 423, 462, 472, 473, 500, 518, 522, 553, 563, 567, 578, 585, 598, 630, 637, 675, 682, 693, 697, 725, 742, 760, 770, 787, 788, 808, 833, 850, 858, 878, 893, 913, 945, 963, 977, 990

Offset

1,1

Comments

See A066272 for definition of anti-divisor.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..576 from Michael De Vlieger)

Example

a(1) = 143 because A066417(143) = 292, which exceeds 2 * 143 = 286. (A066417 is the sum of anti-divisors of n).

Mathematica

a066417[n_Integer] := Total[Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)]]; Select[Range[10000], If[a066417[#] > 2 #, True, False] &] (* Michael De Vlieger, Aug 09 2014 *)

Prog

(Python)
A073954 = [n for n in range(1, 10**5) if sum([d for d in range(2, n, 2) if n%d and not 2*n%d])+sum([d for d in range(3, n, 2) if n%d and 2*n%d in [d-1, 1]]) > 2*n] # Chai Wah Wu, Aug 09 2014

Crossrefs

Cf. A066272 (number of anti-divisors of n), A066417 (sum of anti-divisors of n).

Sequence in context: A217141 A097435 A350735 * A227868 A353059 A176876

Adjacent sequences: A073951 A073952 A073953 * A073955 A073956 A073957

Keyword

easy,nonn

Author

Jason Earls, Sep 03 2002

Status

approved