A338902 Number of integer partitions of the n-th semiprime into semiprimes.

1, 1, 1, 2, 3, 2, 4, 7, 7, 10, 17, 25, 21, 34, 34, 73, 87, 103, 149, 176, 206, 281, 344, 479, 725, 881, 1311, 1597, 1742, 1841, 2445, 2808, 3052, 3222, 6784, 9298, 11989, 14533, 15384, 17414, 18581, 19680, 28284, 35862, 38125, 57095, 60582, 64010, 71730, 76016

Offset: 1

Author

Gus Wiseman, Nov 24 2020

Keywords

• nonn

Comments

A semiprime (A001358) is a product of any two prime numbers.

Examples

			The a(1) = 1 through a(33) = 17 partitions of 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, where A-Z = 10-35:
  4  6  9  A   E    F   L     M      P      Q       X
           64  A4   96  F6    994    FA     M4      EA9
               644      966   A66    L4     AA6     F99
                        9444  E44    A96    E66     FE4
                              6664   F64    9944    L66
                              A444   9664   A664    P44
                              64444  94444  E444    9996
                                            66644   AA94
                                            A4444   E964
                                            644444  F666
                                                    FA44
                                                    L444
                                                    96666
                                                    A9644
                                                    F6444
                                                    966444
                                                    9444444
		

Crossrefs

A002100 counts partitions into squarefree semiprimes.

A056768 uses primes instead of semiprimes.

A101048 counts partitions into semiprimes.

A338903 is the squarefree version.

A339112 includes the Heinz numbers of these partitions.

A001358 lists semiprimes, with odd and even terms A046315 and A100484.

A037143 lists primes and semiprimes.

A084126 and A084127 give the prime factors of semiprimes.

A320655 counts factorizations into semiprimes.

A338898/A338912/A338913 give prime indices of semiprimes, with sum/difference/product A176504/A176506/A087794.

A338899/A270650/A270652 give prime indices of squarefree semiprimes.

Cf. A000041, A000607, A006881, A065516, A115392, A128301, A320656, A320732, A320892, A320912, A338915, A338916, A339113.

Programs

Mathematica

nn=100;Table[Length[IntegerPartitions[n,All,Select[Range[nn],PrimeOmega[#]==2&]]],{n,Select[Range[nn],PrimeOmega[#]==2&]}]

Formula

a(n) = A101048(A001358(n)).