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 A284457 Square array whose rows list numbers with the same squarefree kernel (A007947): Transpose of A284311. 8
 2, 4, 3, 8, 9, 5, 16, 27, 25, 6, 32, 81, 125, 12, 7, 64, 243, 625, 18, 49, 10, 128, 729, 3125, 24, 343, 20, 11, 256, 2187, 15625, 36, 2401, 40, 121, 13, 512, 6561, 78125, 48, 16807, 50, 1331, 169, 14, 1024, 19683, 390625, 54, 117649, 80, 14641, 2197, 28, 15 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The first column contains the squarefree numbers A005117; each row lists all numbers having the same prime divisors. If T[m,1] is prime then the row contains the powers of that prime. Yields A182944 if only these rows with prime powers (A000961) are kept. - M. F. Hasler, Mar 27 2017 See A284311 for further details. LINKS Alois P. Heinz, Antidiagonals n = 1..141, flattened FORMULA From Antti Karttunen, Apr 17 2017: (Start) A(n,1) = A005117(1+n), A(n,k) = A065642(A(n,k-1)). [A "dispersion" of A065642.] A(A285329(n), A008479(n)) = n for all n >= 2.(End) EXAMPLE Array starts:     2    4     8     16      32      64      128     3    9    27     81     243     729     2187     5   25   125    625    3125   15625    78125     6   12    18     24      36      48       54     7   49   343   2401   16807  117649   823543    10   20    40     50      80     100      160    ... Row 6 is: T[1,6] = 2*5; T[2,6] = 2^2*5; T[3,6] = 2^3*5; T[4,6] = 2*5^2; T[5,6] = 2^4*5, etc. MATHEMATICA f[n_, k_: 1] := Block[{c = 0, sgn = Sign[k], sf}, sf = n + sgn; While[c < Abs@ k, While[! SquareFreeQ@ sf, If[sgn < 0, sf--, sf++]]; If[sgn < 0, sf--, sf++]; c++]; sf + If[sgn < 0, 1, -1]] (* after Robert G. Wilson v at A005117 *); T[n_, k_] := T[n, k] = Which[And[n == 1, k == 1], 2, k == 1, f@ T[n - 1, k], PrimeQ@ T[n, 1], T[n, 1]^k, True, Module[{j = T[n, k - 1]/T[n, 1] + 1}, While[PowerMod[T[n, 1], j, j] != 0, j++]; j T[n, 1]]]; Table[T[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten PROG (PARI) A284457(m, n)={for(a=2, m^2+1, (core(a)!=a||m--)&&next; m=factor(a)[, 1]; for(k=1, 9e9, factor(k*a)[, 1]==m&&!n--&&return(k*a)))} \\ M. F. Hasler, Mar 27 2017 (Scheme) (define (A284457 n) (A284311bi (A004736 n) (A002260 n))) ;; For A284311bi, see A284311. - Antti Karttunen, Apr 17 2017 CROSSREFS Cf. A284311, A005117, A007947, A065642, A182944. Cf. A008479 (index of the column where n is located), A285329 (of the row). Sequence in context: A304408 A048767 A269851 * A182944 A269385 A252755 Adjacent sequences:  A284454 A284455 A284456 * A284458 A284459 A284460 KEYWORD nonn,tabl AUTHOR Bob Selcoe, Mar 27 2017 EXTENSIONS Edited by M. F. Hasler, Mar 27 2017 STATUS approved

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Last modified March 21 10:00 EDT 2019. Contains 321368 sequences. (Running on oeis4.)