
0, 1, 0, 0, 1, 0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 4, 2, 4, 3, 4, 3, 5, 3, 6, 4, 6, 4, 7, 5, 8, 6, 7, 6, 9, 6, 11, 7, 8, 8, 11, 8, 12, 9, 11, 9, 12, 9, 14, 10, 14, 10, 14, 11, 16, 12, 15, 12, 16, 13, 19, 14, 15, 14, 19, 14, 21, 15, 17, 16, 21, 16, 22, 17, 20, 17, 22, 17, 25, 18, 22, 19, 23, 19
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OFFSET

1,10


LINKS

Donovan Johnson, Table of n, a(n) for n = 1..10000
Index entries for sequences related to Goldbach conjecture
Index entries for sequences related to partitions


FORMULA

a(n) = Sum_{i=1..floor(n/2)} (1  A010051(i)) * (1  A010051(ni)) = Sum_{i=1..floor(n/2)} A005171(i)*A005171(ni).  Wesley Ivan Hurt, Apr 08 2018
a(n) + A061358(n) + A062602(n) = A004526(n).  R. J. Mathar, Sep 10 2021


EXAMPLE

n = 22 has floor(n/2) = 11 partitions of form n = a+b; 3 partitions are of prime+prime [3+19 = 5+17 = 11+11], 3 partitions are of prime+nonprime [2+20 = 7+15 = 13+9], 5 partitions are of nonprime+nonprime [1+21 = 4+18 = 6+16 = 8+14 = 10+12]. So a(22) = 5.


MATHEMATICA

Table[Count[Transpose@ {#, n  #} &@ Range[Floor[n/2]], w_ /; Times @@ Boole@ Map[! PrimeQ@ # &, w] == 1], {n, 83}] (* Michael De Vlieger, Jul 04 2016 *)


CROSSREFS

Cf. A010051, A014092, A061358, A062602.
Sequence in context: A241061 A103858 A010554 * A351593 A025801 A060548
Adjacent sequences: A062607 A062608 A062609 * A062611 A062612 A062613


KEYWORD

nonn,easy


AUTHOR

Labos Elemer, Jul 04 2001


STATUS

approved

