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Search: id:A083710
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| A083710 |
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Number of partitions of n each of which has a summand which divides every summand in the partition. |
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+0
9
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| 1, 1, 2, 3, 5, 6, 11, 12, 20, 25, 37, 43, 70, 78, 114, 143, 196, 232, 330, 386, 530, 641, 836, 1003, 1340, 1581, 2037, 2461, 3127, 3719, 4746, 5605, 7038, 8394, 10376, 12327, 15272, 17978, 22024, 26095, 31730, 37339, 45333, 53175, 64100, 75340, 90138
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The first few partitions that fail the criterion are 5=3+2, 7=5+2=4+3=3+2+2. So a(5) = A000041(5) - 1 = 6, a(7) = A000041(7) - 3 = 12. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jun 17 2003
Equals left border of triangle A137587 starting (1, 2, 3, 5, 6, 11,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 27 2008
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REFERENCES
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L. M. Chawla, M. O. Levan and J. E. Maxfield, On a restricted partition function and its tables, J. Natur. Sci. and Math., 12 (1972), 95-101.
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MAPLE
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with(combinat): with(numtheory): a := proc(n) c := 0: l := sort(convert(divisors(n), list)): for i from 1 to nops(l)-0 do c := c+numbpart(l[i]-1) od: RETURN(c): end: for j from 0 to 60 do printf(`%d, `, a(j)) od: - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 14 2007
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CROSSREFS
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Cf. A083711, A018783.
Cf. A137587.
Sequence in context: A018255 A018727 A033159 this_sequence A127524 A117086 A081026
Adjacent sequences: A083707 A083708 A083709 this_sequence A083711 A083712 A083713
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KEYWORD
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nonn,easy
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AUTHOR
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njas, Jun 16 2003
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Jun 17 2003
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