

A214771


a(n) is the smallest number that can be written as the sum of consecutive positive integers in at least n ways.


1



3, 9, 15, 45, 45, 105, 105, 225, 315, 315, 315, 945, 945, 945, 945, 1575, 1575, 2835, 2835, 3465, 3465, 3465, 3465, 10395, 10395, 10395, 10395, 10395, 10395, 10395, 10395, 17325, 17325, 17325, 17325, 31185, 31185, 31185, 31185, 45045, 45045, 45045, 45045
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OFFSET

1,1


COMMENTS

The number of forms of writing a number x with odd prime factors as distinct sums of at least two nonzero summands of consecutive positive integers is : d(2x)/2 1 = d(x)  1, where d(x) is the number of divisors of x.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..200


EXAMPLE

a(1) = 3 = 1+2
a(2) = 9 = 4+5 = 2+3+4
a(3) = 15 = 7+8 = 4+5+6 = 1+2+3+4+5
a(4) = a(5) = 45 is the sum of 2,3,5,6 and 9 consecutive integers beginning with 22, 14, 7, 5 and 1 respectively.


MATHEMATICA

nn = 50000; t = Table[0, {nn}]; Do[tot = i; j = i; While[j++; tot = tot + j; tot <= nn, t[[tot]]++], {i, nn/2  1}]; Table[Position[t, _?(# >= n &), 1, 1][[1, 1]], {n, Max[t]}] (* T. D. Noe, Jul 28 2012 *)


CROSSREFS

Cf. A053624 (union of these terms), A057716 (not powers of 2).
Sequence in context: A057909 A228916 A082702 * A065917 A053624 A119239
Adjacent sequences: A214768 A214769 A214770 * A214772 A214773 A214774


KEYWORD

nonn


AUTHOR

Robin Garcia, Jul 27 2012


EXTENSIONS

Definition corrected by Jonathan Sondow, Feb 19 2014


STATUS

approved



