id:A103840 - OEIS Search Results

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Number of ways to represent n as a sum of b^e with b >= 2, e >= 2, e distinct.

+0
2

1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 2, 2, 0, 1, 1, 0, 0, 1, 2, 2, 0, 0, 3, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 1, 2, 3, 0, 0, 4, 0, 0, 0, 2, 3, 0, 2, 2, 0, 0, 2, 4, 3, 0, 0, 5, 0, 0, 0, 3, 4, 0, 2, 3, 0, 0, 2, 5, 5, 0, 0, 5, 1, 0, 0, 3, 7, 1, 3, 3, 1, 0, 2, 5, 5, 1, 0, 7, 0, 0, 0, 3 (list; graph; listen)

	OFFSET	`1,17`
	COMMENT	`291 is the largest number that cannot be expressed in this way.`
	FORMULA	`G.f.: Prod(e >= 2, 1 + Sum(b >= 2, x^(b^e))).`
	EXAMPLE	`68 = 2^2+4^3 = 2^2+2^6 = 3^2+3^3+2^5 = 5^2+3^3+2^4 = 6^2+2^5 so a(68) = 5. Note that although 4^3 = 2^6, the exponents are different, and so 2^2+4^3 and 2^2+2^6 are counted as distinct.`
	CROSSREFS	`Cf. A103841 (where a(n) = 0), A103843 (positions of records).` `Sequence in context: A115079 A025435 A081221 this_sequence A066301 A046660 A108730` `Adjacent sequences: A103837 A103838 A103839 this_sequence A103841 A103842 A103843`
	KEYWORD	`nonn`
	AUTHOR	`Gordon Hamilton (hamiltonian(AT)shaw.ca), Mar 29 2005`
	EXTENSIONS	`More terms from David W. Wilson (davidwwilson(AT)comcast.net), Mar 30 2005` `More terms from David Wasserman (dwasserm(AT)earthlink.net), Apr 24 2008`

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.

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