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 A284061 Triangle read by rows: T(n,k) = pi(prime(k) * prime(n+1)). 1
 3, 4, 6, 6, 8, 11, 8, 11, 16, 21, 9, 12, 18, 24, 34, 11, 15, 23, 30, 42, 47, 12, 16, 24, 32, 46, 53, 66, 14, 19, 30, 37, 54, 62, 77, 84, 16, 23, 34, 46, 66, 74, 94, 101, 121, 18, 24, 36, 47, 68, 79, 99, 107, 127, 154, 21, 29, 42, 55, 79, 92, 114, 126, 146, 180 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Prime(T(n,k)) is the largest prime q such that q * p_n# / prime(k) < p_(n+1)#, with primorial p_n# = A002110(n). T(n,1) = A020900(n+1), T(n,2) = A020901(n+1), T(n,3) = A020935(n+1), T(n,4) = A020937(n+1). LINKS Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1 <= n <= 150). EXAMPLE a(5) = T(2,2) = 8 since the largest prime q <= prime(2) prime(3+1) = 3*7 = 21 is 19, the 8th prime. Rows 1 <= n <= 12 of triangle T(n,k):    3    4    6    6    8   11    8   11   16   21    9   12   18   24   34   11   15   23   30   42   47   12   16   24   32   46   53    66   14   19   30   37   54   62    77    84   16   23   34   46   66   74    94   101   121   18   24   36   47   68   79    99   107   127   154   21   29   42   55   79   92   114   126   146   180   189   22   30   46   61   87   99   125   137   160   195   205   240 Values of m = q * p_n#/prime(k) < p_(n+1)# with q = prime(T(n,k)):                                     prime(k)                       2       3       5       7      11      13            6  |       5           30  |      21      26 p_(n+1)# 210  |     195     190     186         2310  |    1995    2170    2226    2190        30030  |   26565   28490   28182   29370   29190       510510  |  465465  470470  498498  484770  494130  487410 All terms m of row n have omega(m) = A001221(m) = n. MATHEMATICA Table[PrimePi[Prime[k] Prime[n + 1]], {n, 11}, {k, n}] // Flatten PROG (PARI) for(n=1, 12, for(k=1, n, print1(primepi(prime(k) * prime(n + 1)), ", "); ); print(); ); \\ Indranil Ghosh, Mar 19 2017 (Python) from sympy import prime, primepi for n in xrange(1, 13): ....print[primepi(prime(k) * prime(n + 1)) for k in xrange(1, n+1)] # Indranil Ghosh, Mar 19 2017 CROSSREFS Cf. A020900, A020901, A020935, A020937. Sequence in context: A230300 A275883 A274529 * A162625 A033095 A158907 Adjacent sequences:  A284058 A284059 A284060 * A284062 A284063 A284064 KEYWORD nonn,tabl,easy AUTHOR Michael De Vlieger, Mar 19 2017 STATUS approved

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Last modified February 19 21:04 EST 2019. Contains 320328 sequences. (Running on oeis4.)