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 A283529 The number of partitions of n into simple parts. 2
 1, 1, 2, 2, 3, 3, 5, 5, 7, 7, 9, 9, 12, 12, 15, 15, 18, 18, 22, 22, 26, 26, 30, 30, 35, 35, 40, 40, 45, 45, 52, 52, 59, 59, 66, 66, 75, 75, 84, 84, 93, 93, 104, 104, 115, 115, 126, 126, 139, 139, 152, 152, 165, 165, 180, 180, 195, 195, 210, 210, 228, 228 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Number of partitions of n where each part is simple, meaning that each part is in A002110. LINKS Giovanni Resta, Table of n, a(n) for n = 0..10000 J. Wang, Reduced phi-partitions of positive integers, Fib. Quart. 31 (4) (1993) 365-369. FORMULA G.f.: 1/Product_{i>=0} (1-x^A002110(i)). EXAMPLE a(6)=5 counts 1+1+1+1+1+1 = 1+1+1+2 = 1+1+2+2 = 2+2+2 =6. a(7)=5 counts 1+1+1+1+1+1+1 = 1+1+1+1+1+2 = 1+1+1+2+2 = 1+2+2+2 = 1+6. MAPLE isA002110 := proc(n)     member(n, [1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230, 200560490130, 7420738134810, 304250263527210, 13082761331670030, 614889782588491410, 32589158477190044730, 1922760350154212639070]) ; end proc: A283529 := proc(n)     local a, k, issimp, p ;     a := 0 ;     for k in combinat[partition](n) do         issimp := true ;         for p in k do             if not isA002110(p) then                 issimp := false;                 break;             end if;         end do:         if issimp then             a := a+1 ;         end if;     end do:     a ; end proc: MATHEMATICA (* It suffices to compute 3 primorials to get 100 correct terms *) terms = 100; primorials = FoldList[Times, 1, Prime[Range[3]]]; 1/(Times @@ (1 - x^primorials)) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, May 19 2018 *) CROSSREFS Cf. A002110, A064986, A283528. Sequence in context: A085885 A309685 A309683 * A064986 A349675 A029019 Adjacent sequences:  A283526 A283527 A283528 * A283530 A283531 A283532 KEYWORD nonn AUTHOR R. J. Mathar, Mar 10 2017 EXTENSIONS a(0)=1 prepended by Alois P. Heinz, Mar 13 2017 STATUS approved

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Last modified December 4 05:56 EST 2021. Contains 349470 sequences. (Running on oeis4.)