Search: id:A002095
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%I A002095 M0271 N0094
%S A002095 1,1,1,1,2,2,3,3,5,6,8,8,12,13,17,19,26,28,37,40,52,58,73,79,102,113,
%T A002095 139,154,191,210,258,284,345,384,462,509,614,679,805,893,1060,1171,
%U A002095 1382,1528,1792,1988,2319,2560,2986,3304,3823,4231,4888,5399,6219,6870
%N A002095 Number of partitions of n into nonprime parts.
%C A002095 Partial sums of A023895. - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Apr 19 2006
%D A002095 L. M. Chawla and S. A. Shad, On a trio-set of partition functions and 
               their tables, J. Natural Sciences and Mathematics, 9 (1969), 87-96.
%D A002095 A. Murthy, Some new Smarandache sequences, functions and partitions, 
               Smarandache Notions Journal Vol. 11 N. 1-2-3 Spring 2000 (but beware 
               errors).
%D A002095 Amarnath Murthy and Charles Ashbacher, Generalized Partitions and Some 
               New Ideas on Number Theory and Smarandache Sequences, Hexis, Phoenix; 
               USA 2005. See Section 2.6.
%D A002095 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002095 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A002095 T. D. Noe, <a href="b002095.txt">Table of n, a(n) for n=0..1000</a>
%F A002095 G.f.: Product_{i>0} (1-x^prime(i))/(1-x^i). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Jul 31 2004
%e A002095 a(6) = 3 from the partitions 6=1+1+1+1+1+1=4+1+1.
%p A002095 g:=product((1-x^ithprime(j))/(1-x^j),j=1..60): gser:=series(g,x=0,60): 
               seq(coeff(gser,x,n),n=0..55); - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Apr 19 2006
%t A002095 NonPrime[n_Integer] := FixedPoint[n + PrimePi[ # ] &, n + PrimePi[n]]; 
               CoefficientList[ Series[1/Product[1 - x^NonPrime[i], {i, 1, 50}], 
               {x, 0, 50}], x]
%Y A002095 Cf. A000607, A018252.
%Y A002095 Sequence in context: A062303 A050318 A130841 this_sequence A029017 A035371 
               A035577
%Y A002095 Adjacent sequences: A002092 A002093 A002094 this_sequence A002096 A002097 
               A002098
%K A002095 nonn,easy,nice
%O A002095 0,5
%A A002095 N. J. A. Sloane (njas(AT)research.att.com).
%E A002095 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 23 1999
%E A002095 Corrected by Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 11 2002

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