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 A096436 a(n) = the number of squared primes and 1's needed to sum to n. 3
 1, 2, 3, 1, 2, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 2, 3, 4, 4, 3, 4, 5, 1, 2, 3, 4, 2, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 3, 4, 5, 5, 4, 5, 1, 2, 3, 4, 2, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 3, 4, 5, 5, 4, 5, 6, 2, 3, 4, 5, 3, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 6, 5, 4, 5, 6, 6, 5, 6, 2, 3, 4, 5, 3, 4, 5, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) has a new maximum at n=1,2,3,7,24,73,266,795. I suspect that a(n) <= 9 for all n. - Robert G. Wilson v, Sep 18 2004 LINKS EXAMPLE a(5) = 2 because 5=4+1. a(17) = 3 because 17=9+4+4. A number may have many such sums: 27=25+1+1=9+9+9, 50=25+25=49+1. MATHEMATICA f[n_] := Block[{d = n, k = PrimePi[ Sqrt[n]], sp = {}}, While[d > 3, While[p = Prime[k]; d >= p^2, AppendTo[sp, p]; d = d - p^2]; k-- ]; While[d != 0, AppendTo[sp, 1]; d = d - 1]; If[Position[sp, 3] != {} && sp[[ -3]] == 1, sp = Delete[Drop[sp, -3], Position[sp, 3][[1]]]; AppendTo[sp, {2, 2, 2}]]; Reverse[ Sort[ Flatten[ sp]]]]; Table[ Length[ f[n]], {n, 105}] (* Robert G. Wilson v, Sep 20 2004 *) CROSSREFS Cf. A001248, A002828, A045698, A051034, A063274. Sequence in context: A002828 A191091 A098066 * A053610 A264031 A104246 Adjacent sequences:  A096433 A096434 A096435 * A096437 A096438 A096439 KEYWORD nonn,easy AUTHOR Tom Raes (tommy1729(AT)hotmail.com), Aug 10 2004 EXTENSIONS Edited and extended by Robert G. Wilson v, Sep 18 2004 Edited by Don Reble, Apr 23 2006 STATUS approved

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Last modified October 14 01:36 EDT 2019. Contains 327994 sequences. (Running on oeis4.)