A082637 a(n) = smallest number which can be expressed as sum of d consecutive positive integers in exactly n ways (where d>0 is a divisor of the number).

1, 6, 15, 45, 135, 378, 315, 630, 945, 1575, 2205, 3150, 4095, 3465, 9450, 6930, 13860, 10395, 17955, 17325, 33075, 31185, 97020, 62370, 99225, 45045, 61425, 51975, 103950, 143325, 207900, 180180, 155925, 184275, 176715, 135135, 579150, 353430

Offset

1,2

Links

Donovan Johnson, Table of n, a(n) for n = 1..300

Example

For n=3: 15 is in the sequence because 15 has three ways: e.g. (d=3; 3|15) and 4+5+6=15, (d=5; 5|15) and 1+2+3+4+5=15, (d=1; 1|15) and 15=15. 15 is the smallest number. so a(3)=15.

Prog

(PARI) divCount(n) = local(count, d, m, dd); count = 1; d = divisors(n); m = matsize(d)[2]; for (i = 2, m, dd = d[i]; if (dd*(dd + 1)/2 > n, return(count)); if (dd%2, if (n%dd == 0, count = count + 1), if (n%dd == dd/2, count = count + 1))); return(count); A = vector(45); count = 0; i = 0; while (count < 45, i = i + 1; n = divCount(i); if (A[n] == 0, A[n] = i; count = count + 1; )); A

Crossrefs

Cf. A082636.

Sequence in context: A318482 A095122 A215917 * A244023 A271131 A271154

Adjacent sequences: A082634 A082635 A082636 * A082638 A082639 A082640

Keyword

nonn

Author

Naohiro Nomoto, May 14 2003

Extensions

More terms from David Wasserman, Sep 23 2004

Status

approved