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 A317390 A(n,k) is the n-th positive integer that has exactly k representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes; square array A(n,k), n>=1, k>=0, read by antidiagonals. 14
 2, 1, 5, 25, 3, 7, 43, 29, 4, 11, 211, 61, 37, 6, 15, 638, 261, 91, 40, 8, 23, 664, 848, 421, 111, 41, 9, 26, 1613, 1956, 921, 426, 121, 49, 10, 27, 2991, 3321, 2058, 969, 441, 124, 51, 12, 28, 7021, 3004, 3336, 2092, 1002, 484, 171, 52, 13, 31, 11306, 7162, 3319, 3368, 2094, 1026, 535, 184, 67, 14, 33 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Alois P. Heinz, Antidiagonals n = 1..34, flattened Index entries for sequences that are permutations of the natural numbers FORMULA A317241(A(n,k)) = k. EXAMPLE A(6,2) = 49: 1 + 3 * (1 + 5 * (1 + 2)) = 1 + 2 * (1 + 23) = 49. Square array A(n,k) begins: 2, 1, 25, 43, 211, 638, 664, 1613, 2991, ... 5, 3, 29, 61, 261, 848, 1956, 3321, 3004, ... 7, 4, 37, 91, 421, 921, 2058, 3336, 3319, ... 11, 6, 40, 111, 426, 969, 2092, 3368, 3554, ... 15, 8, 41, 121, 441, 1002, 2094, 3741, 3928, ... 23, 9, 49, 124, 484, 1026, 2283, 3914, 4846, ... 26, 10, 51, 171, 535, 1106, 2381, 3979, 5552, ... 27, 12, 52, 184, 540, 1156, 2388, 4082, 5886, ... 28, 13, 67, 187, 591, 1191, 2432, 4126, 6293, ... MAPLE b:= proc(n, s) option remember; `if`(n=1, 1, add(b((n-1)/p, s union {p}) , p=numtheory[factorset](n-1) minus s)) end: A:= proc() local h, p, q; p, q:= proc() [] end, 0; proc(n, k) while nops(p(k))

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Last modified September 15 02:25 EDT 2024. Contains 375929 sequences. (Running on oeis4.)