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%I #5 Aug 04 2022 22:27:40
%S 1,1,3,6,10,19,37,74,140,269,520,1026,1984,3831,7368,14302,27707,
%T 53729,103826,201035,389094,753858,1458852,2824336,5466167,10584567,
%U 20489682,39669401,76787404,148660956,287786132,557153147,1078562051,2088027468
%N Coefficients in the series (1 + 2x^2 + 3x^3 + 5x^5 + 7x^7 + 11x^11 + 13x^13 + ... )/(1 - x - 4x^4 - 6x^6 - 8x^8 - 9x^9 - 10x^10 - 12x^12 - 14x^14 - ... ).
%t CoefficientList[ Series[ (1 + Apply[ Plus, Select[ Range[ 2, 50 ], PrimeQ[ # ] & ]*x^Select[ Range[ 2, 50 ], PrimeQ[ # ] & ] ] ) / (1 - Apply[ Plus, Select[ Range[ 1, 50 ], !PrimeQ[ # ] & ]*x^Select[ Range[ 1, 50 ], !PrimeQ[ # ] & ] ] ), {x, 0, 40} ], x ]
%K nonn
%O 0,3
%A _Robert G. Wilson v_, Dec 16 2000
%E Name corrected by _Sean A. Irvine_, Aug 04 2022