

A145265


A positive integer n is included if there exists a positive integer m such that Sum_{k>=0} floor(n/(m+k)) = n.


2



1, 4, 5, 8, 15, 18, 19, 22, 23, 26, 33, 36, 37, 40, 41, 44, 51, 54, 55, 58, 59, 62, 69, 72, 73, 76, 77, 80, 87, 90, 91, 94, 95, 98, 105, 108, 109, 112, 113, 116, 123, 126, 127, 130, 131, 134, 141, 144, 145, 148, 149, 152, 159, 162, 163, 166, 167, 170, 177, 180, 181, 184
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OFFSET

1,2


COMMENTS

This sequence is the complement of sequence A145266. A145264(a(n)) >= 1.
Does this sequence contain all of those and only those, positive integers that are congruent to 0, 1, 4, 5, 8, 15 (mod 18)?  Leroy Quet, Oct 31 2008
This sequence and its crossreferents may be calculated more easily by checking whether a partial sum of sum{k>=0} floor(n/(nk)) ever equals n; that is, calculating from the top down. It appears that the terms are precisely those congruent to 0, 1, 4, 5, 8, or 15 modulo 18.  Bryce Herdt (mathidentity(AT)yahoo.com), Nov 02 2008


LINKS

Table of n, a(n) for n=1..62.
Leroy Quet, sum{k>=m} floor(n/k) = n, rec.puzzles [From Bryce Herdt (mathidentity(AT)yahoo.com), Nov 02 2008]


EXAMPLE

Checking n = 8: floor(8/3) + floor(8/4) + floor(8/5) + floor(8/6) + floor(8/7) + floor(8/8) = 2 + 2 + 1 + 1 + 1 + 1 = 8. So 8 is included in the sequence. Checking n = 6: floor(6/2) + floor(6/3) + floor(6/4) + floor(6/5) + floor(6/6) = 3 + 2 + 1 + 1 + 1 = 8, which is > 6. But floor(6/3) + floor(6/4) + floor(6/5) + floor(6/6) = 2 + 1 + 1 + 1 = 5, which is < 6. So 6 is not included in the sequence.


MATHEMATICA

a = {}; For[n = 1, n < 200, n++, c = 0; For[m = 1, m < n + 1, m++, If[Sum[Floor[n/(m + k)], {k, 0, n}] == n, c = 1; Break]]; If[c == 1, AppendTo[a, n]]]; a (* Stefan Steinerberger, Oct 17 2008 *)


CROSSREFS

Cf. A145264, A145266.
Sequence in context: A145488 A050892 A274167 * A244161 A258935 A275929
Adjacent sequences: A145262 A145263 A145264 * A145266 A145267 A145268


KEYWORD

nonn


AUTHOR

Leroy Quet, Oct 05 2008


EXTENSIONS

More terms from Stefan Steinerberger, Oct 17 2008


STATUS

approved



