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 A328464 Square array A(n,k) = A276156((2^(n-1)) * (2k-1)) / A002110(n-1), read by descending antidiagonals. 12
 1, 3, 1, 7, 4, 1, 9, 16, 6, 1, 31, 19, 36, 8, 1, 33, 106, 41, 78, 12, 1, 37, 109, 386, 85, 144, 14, 1, 39, 121, 391, 1002, 155, 222, 18, 1, 211, 124, 421, 1009, 2432, 235, 324, 20, 1, 213, 1156, 426, 1079, 2443, 4200, 341, 438, 24, 1, 217, 1159, 5006, 1086, 2575, 4213, 7430, 457, 668, 30, 1, 219, 1171, 5011, 17018, 2586, 4421, 7447, 12674, 691, 900, 32, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Array is read by falling antidiagonals with n (row) and k (column) ranging as: (n,k) = (1,1), (1,2), (2,1), (1,3), (2,2), (3,1), ... Row n contains all such sums of distinct primorials whose least significant summand is A002110(n-1), with each sum divided by that least significant primorial, which is also the largest primorial which divides that sum. LINKS FORMULA A(n,k) = A276156((2^(n-1)) * (2k-1)) / A002110(n-1). a(n) = A328461(A135764(n)). [When all sequences are considered as one-dimensional] EXAMPLE Top left 9 X 11 corner of the array: 1: | 1,  3,   7,   9,    31,    33,    37,    39,    211,    213,    217 2: | 1,  4,  16,  19,   106,   109,   121,   124,   1156,   1159,   1171 3: | 1,  6,  36,  41,   386,   391,   421,   426,   5006,   5011,   5041 4: | 1,  8,  78,  85,  1002,  1009,  1079,  1086,  17018,  17025,  17095 5: | 1, 12, 144, 155,  2432,  2443,  2575,  2586,  46190,  46201,  46333 6: | 1, 14, 222, 235,  4200,  4213,  4421,  4434,  96578,  96591,  96799 7: | 1, 18, 324, 341,  7430,  7447,  7753,  7770, 215442, 215459, 215765 8: | 1, 20, 438, 457, 12674, 12693, 13111, 13130, 392864, 392883, 393301 9: | 1, 24, 668, 691, 20678, 20701, 21345, 21368, 765050, 765073, 765717 PROG (PARI) up_to = 105; A002110(n) = prod(i=1, n, prime(i)); A276156(n) = { my(p=2, pr=1, s=0); while(n, if(n%2, s += pr); n >>= 1; pr *= p; p = nextprime(1+p)); (s); }; A328464sq(n, k) = (A276156((2^(n-1)) * (k+k-1)) / A002110(n-1)); A328464list(up_to) = { my(v = vector(up_to), i=0); for(a=1, oo, for(col=1, a, i++; if(i > up_to, return(v)); v[i] = A328464sq(col, (a-(col-1))))); (v); }; v328464 = A328464list(up_to); A328464(n) = v328464[n]; CROSSREFS Cf. A328463 (transpose). Cf. A000265, A002110, A007814, A135764, A276154, A276156, Rows 1 - 5: A328462, A328465, A328466, A328467, A328468. Column 2: A008864. Column 3: A023523 (after its initial term). Column 4: A286624. Cf. also arrays A276945, A286625. Sequence in context: A095868 A140962 A013602 * A323956 A086272 A104709 Adjacent sequences:  A328461 A328462 A328463 * A328465 A328466 A328467 KEYWORD nonn,tabl AUTHOR Antti Karttunen, Oct 16 2019 STATUS approved

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Last modified June 19 09:33 EDT 2021. Contains 345126 sequences. (Running on oeis4.)