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Search: id:A082637
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| A082637 |
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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). |
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+0
4
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| 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
(list; graph; listen)
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OFFSET
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1,2
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EXAMPLE
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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.
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PROGRAM
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(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
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CROSSREFS
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Cf. A082636.
Adjacent sequences: A082634 A082635 A082636 this_sequence A082638 A082639 A082640
Sequence in context: A100491 A117961 A095122 this_sequence A106272 A051169 A051610
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KEYWORD
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nonn
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AUTHOR
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Naohiro Nomoto (n_nomoto(AT)yabumi.com), May 14 2003
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Sep 23 2004
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