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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). 4

%I

%S 1,6,15,45,135,378,315,630,945,1575,2205,3150,4095,3465,9450,6930,

%T 13860,10395,17955,17325,33075,31185,97020,62370,99225,45045,61425,

%U 51975,103950,143325,207900,180180,155925,184275,176715,135135,579150,353430

%N 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).

%H Donovan Johnson, <a href="/A082637/b082637.txt">Table of n, a(n) for n = 1..300</a>

%e 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.

%o (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

%Y Cf. A082636.

%K nonn

%O 1,2

%A _Naohiro Nomoto_, May 14 2003

%E More terms from _David Wasserman_, Sep 23 2004

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Last modified February 26 09:05 EST 2020. Contains 332277 sequences. (Running on oeis4.)