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 A064572 Number of ways to partition n into parts which are all powers of some integer k. 6
 0, 1, 2, 5, 6, 10, 11, 17, 20, 26, 27, 38, 39, 47, 51, 65, 66, 82, 83, 102, 107, 123, 124, 153, 156, 178, 185, 216, 217, 254, 255, 297, 304, 342, 346, 408, 409, 457, 466, 535, 536, 609, 610, 690, 704, 780, 781, 895, 898, 998, 1009, 1130, 1131, 1263, 1268, 1418 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Number of ways to partition n as Sum_i k^e_i, where the exponents e_i are not all 0. The exponents cannot all be 0, e.g. a(2)=1 arises from 2^1, and does not include 2^0+2^0. - Shujing Lyu, Apr 23 2016 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1000 (terms 1..220 from Shujing Lyu) FORMULA G.f.: Sum_{k>=2} 1/(Product_{r>=0} 1-x^(k^r)) - 1/(1-x). - Andrew Howroyd, Dec 29 2017 EXAMPLE a(4)=5: 4^1, 3^1+3^0, 2^2, 2*2^1, 2^1+2*2^0. PROG (PARI) first(n)={Vec(sum(k=2, n, 1/prod(r=0, logint(n, k), 1-x^(k^r) + O(x*x^n)) - 1/(1-x), 0), -n)} \\ Andrew Howroyd, Dec 29 2017 CROSSREFS Cf. A028422, A064573, A064574, A064575, A064576, A064577, A292477. Sequence in context: A077471 A273324 A238096 * A032399 A276496 A007969 Adjacent sequences:  A064569 A064570 A064571 * A064573 A064574 A064575 KEYWORD easy,nonn AUTHOR Marc LeBrun, Sep 20 2001 STATUS approved

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Last modified July 25 13:05 EDT 2021. Contains 346290 sequences. (Running on oeis4.)