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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 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.)