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Search: id:A049822
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| A049822 |
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a(n) = 1-tau(n)+Sum_{d|n} tau(d-1). |
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+0
4
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| 0, 0, 1, 1, 2, 2, 3, 2, 4, 4, 3, 4, 5, 4, 6, 5, 4, 6, 5, 6, 9, 6, 3, 6, 9, 7, 7, 8, 5, 10, 7, 6, 9, 7, 8, 11, 8, 6, 9, 10, 7, 12, 7, 8, 14, 8, 3, 10, 12, 13, 10, 11, 5, 10, 12, 12, 13, 8, 3, 14, 11, 8, 15, 11, 13, 16, 7, 9, 9, 14, 7, 14, 11, 9, 16, 12, 11, 15, 7, 14, 16, 11, 3, 18, 17, 10, 9, 12
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OFFSET
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1,5
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COMMENT
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Number of partitions of n into 3 summands 0<a<=b<=c with b/a and c/b integers.
a(n)=number of 1's in n-th row of array T given by A049816. E.g. there are 5 numbers k from 1 to 13 for which the Euclidean algorithm on (13,k) has exactly 1 nonzero remainder; hence a(13)=5.
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EXAMPLE
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a(6) = 2 because of the 3 partitions of 6 into 3 parts, [4,1,1] and [2,2,2] meet the definition; [3,2,1] fails because 2 does not divide 3.
a(100)=20 because there are 20 partitions of 100 in 3 summands 0<a<=b<=c with integer b/a and c/b: {a, b, c}={1, 1, 98}, {1, 3, 96}, {1, 9, 90}, {1, 11, 88}, {1, 33, 66}, {2, 2, 96}, {2, 14, 84}, {4, 4, 92}, {4, 8, 88}, {4, 12, 84}, {4, 16, 80}, {4, 24, 72}, {4, 32, 64}, {4, 48, 48}, {5, 5, 90}, {10, 10, 80}, {10, 30, 60}, {20, 20, 60}, {20, 40, 40}, {25, 25, 50}.
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CROSSREFS
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Column 3 of A122934. Cf. A003238, A057427, A000005.
Cf. A069905 Number of partitions of n into 3 positive parts.
Sequence in context: A051693 A115980 A088936 this_sequence A140060 A164341 A124771
Adjacent sequences: A049819 A049820 A049821 this_sequence A049823 A049824 A049825
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KEYWORD
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easy,nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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Additional comments from Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 23 2003, Zak Seidov (zakseidov(AT)yahoo.com), Aug 31 2006 and Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Sep 20 2006
Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 21 2006
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