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A338902 Number of integer partitions of the n-th semiprime into semiprimes. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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

LINKS

Table of n, a(n) for n=1..50.

FORMULA

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

EXAMPLE

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

MATHEMATICA

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

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.

Sequence in context: A207606 A303845 A132439 * A116217 A333907 A274486

Adjacent sequences:  A338899 A338900 A338901 * A338903 A338904 A338905

KEYWORD

nonn

AUTHOR

Gus Wiseman, Nov 24 2020

STATUS

approved

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Last modified June 24 08:30 EDT 2021. Contains 345416 sequences. (Running on oeis4.)