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Search: id:A081530
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| A081530 |
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a(n) = running sum of the first n harmonic numbers, multiplied by LCM of 1..n. |
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+0
3
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| 1, 5, 26, 77, 522, 669, 5772, 13827, 48610, 55991, 699612, 785633, 11359222, 12530955, 13726712, 29889983, 550271934, 593094837, 12094689300, 12932216325, 13780828710, 14640022575, 356714770680, 376932115005, 1986818142426
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Consider triangle in A081525. Write terms in k-th row with denominator = lcm of terms in that row. Sequence gives sum of numerators of terms in n-th row.
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FORMULA
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a(n)=LCM(1, .., n)*(n+1)*(H(n+1)-1), where H(n) is the n-th harmonic number. - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004
Equal to A001705(n) / A025527(n). - Martin Fuller (martin_n_fuller(AT)btinternet.com), Jan 03 2006
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EXAMPLE
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(1), 2*((1)+(3/2)), 6*((1)+(3/2)+(11/6)), 12*((1)+(3/2)+(11/6)+(25/12))
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MAPLE
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H:=n->add(1/i, i=1..n):seq((n+1)*ilcm(seq(j, j=1..n))*(H(n+1)-1), n=1..30); (C. Ronaldo)
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MATHEMATICA
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Table[Sum[HarmonicNumber[k], {k, n}] LCM @@ Range[n], {n, 36}] (Meeussen)
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CROSSREFS
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Cf. A081525, A081526, A081527, A081528, A081529.
Cf. A001705, A025527.
Sequence in context: A139273 A048395 A081886 this_sequence A145013 A096943 A166810
Adjacent sequences: A081527 A081528 A081529 this_sequence A081531 A081532 A081533
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 27 2003
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EXTENSIONS
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More terms from Wouter Meeussen (wouter.meeussen(AT)pandora.be), Apr 13 2003
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