

A256562


Number of deficient numbers <= n.


1



1, 2, 3, 4, 5, 5, 6, 7, 8, 9, 10, 10, 11, 12, 13, 14, 15, 15, 16, 16, 17, 18, 19, 19, 20, 21, 22, 22, 23, 23, 24, 25, 26, 27, 28, 28, 29, 30, 31, 31, 32, 32, 33, 34, 35, 36, 37, 37, 38, 39, 40, 41, 42, 42, 43, 43, 44, 45, 46, 46, 47, 48, 49, 50, 51, 51, 52, 53
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000
Marc Deléglise, Bounds for the density of abundant integers, Experiment. Math. Volume 7, Issue 2 (1998), 137143.
Charles R. Wall, Phillip L. Crews and Donald B. Johnson, Density bounds for the sum of divisors function, Math. Comp. 26 (1972), 773777.
Eric Weisstein's World of Mathematics, Abundant Number


EXAMPLE

For k=1 to 5, all numbers are deficients so a(k) = k in this range.
a(6) = 5 since 6 is the first number that is not deficient.


MATHEMATICA

a[n_]:=Length[Select[Range[n], DivisorSigma[1, #]/#<2&]]; a/@Range[68] (* Ivan N. Ianakiev, Apr 03 2015 *)


PROG

(PARI) a(n) = sum(k=1, n, sigma(k)/k < 2);
(MAGMA) [#[k:k in [1..n] DivisorSigma(1, k) lt 2*k]:n in [1..70]]; // Marius A. Burtea, Nov 06 2019


CROSSREFS

Cf. A000396 (perfect), A005100 (deficient), A005101 (abundant).
Cf. A091194 (number of abundant numbers <= n).
Cf. A256440.
Sequence in context: A006163 A331268 A053757 * A228297 A303788 A319288
Adjacent sequences: A256559 A256560 A256561 * A256563 A256564 A256565


KEYWORD

nonn


AUTHOR

Michel Marcus, Apr 02 2015


STATUS

approved



