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Search: id:A072720
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| A072720 |
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Number of partitions of n into parts which are each powers of a single number (which may vary between partitions). |
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+0
2
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| 1, 1, 2, 3, 5, 6, 10, 11, 15, 17, 23, 24, 34, 35, 43, 47, 57, 58, 73, 74, 91, 96, 112, 113, 139, 141, 163, 168, 197, 198, 235, 236, 272, 279, 317, 321, 378, 379, 427, 436, 501, 502, 575, 576, 653, 666, 742, 743, 851, 853, 952, 963, 1080, 1081, 1211, 1216, 1361
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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a(n) = a(n-1)+A072721(n). a(p)=a(p-1)+1 for p prime.
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EXAMPLE
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a(6)=10 since 6 can be written as 6 (powers of 6), 5+1 (5), 4+1+1 (4 or 2), 3+3 (3), 3+1+1+1 (3), 4+2 (2), 2+2+2 (2), 2+2+1+1 (2), 2+1+1+1+1 (2) and 1+1+1+1+1+1 (powers of anything).
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CROSSREFS
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Cf. A000123, A005704, A005705, A005706, A072721.
Sequence in context: A076474 A057760 A074243 this_sequence A018396 A003238 A051839
Adjacent sequences: A072717 A072718 A072719 this_sequence A072721 A072722 A072723
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jul 05 2002
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