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
Keywords
Examples
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.
Links
- Donovan Johnson, Table of n, a(n) for n = 1..300
Crossrefs
Cf. A082636.
Programs
-
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
Extensions
More terms from David Wasserman, Sep 23 2004