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A285321 Square array A(1,k) = A019565(k), A(n,k) = A065642(A(n-1,k)), read by descending antidiagonals. 10
2, 3, 4, 6, 9, 8, 5, 12, 27, 16, 10, 25, 18, 81, 32, 15, 20, 125, 24, 243, 64, 30, 45, 40, 625, 36, 729, 128, 7, 60, 75, 50, 3125, 48, 2187, 256, 14, 49, 90, 135, 80, 15625, 54, 6561, 512, 21, 28, 343, 120, 225, 100, 78125, 72, 19683, 1024 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A permutation of the natural numbers > 1.

Otherwise like array A284311, but the columns come in different order.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..120; the first 15 antidiagonals of array

FORMULA

A(1,k) = A019565(k), A(n,k) = A065642(A(n-1,k)).

For all n >= 2: A(A008479(n), A087207(n)) = n.

EXAMPLE

The top left 12x6 corner of the array:

   2,   3,  6,     5,  10,  15,  30,      7,  14,  21,  42,   35

   4,   9, 12,    25,  20,  45,  60,     49,  28,  63,  84,  175

   8,  27, 18,   125,  40,  75,  90,    343,  56, 147, 126,  245

  16,  81, 24,   625,  50, 135, 120,   2401,  98, 189, 168,  875

  32, 243, 36,  3125,  80, 225, 150,  16807, 112, 441, 252, 1225

  64, 729, 48, 15625, 100, 375, 180, 117649, 196, 567, 294, 1715

MATHEMATICA

a065642[n_] := Module[{k}, If[n == 1, Return[1], k = n + 1; While[ EulerPhi[k]/k != EulerPhi[n]/n, k++]]; k];

A[1, k_] := Times @@ Prime[Flatten[Position[#, 1]]]&[Reverse[ IntegerDigits[k, 2]]];

A[n_ /; n > 1, k_] := A[n, k] = a065642[A[n - 1, k]];

Table[A[n - k + 1, k], {n, 1, 10}, {k, n, 1, -1}] // Flatten (* Jean-Fran├žois Alcover, Nov 17 2019 *)

PROG

(Scheme)

(define (A285321 n) (A285321bi (A002260 n) (A004736 n)))

(define (A285321bi row col) (if (= 1 row) (A019565 col) (A065642 (A285321bi (- row 1) col))))

(Python)

from operator import mul

from sympy import prime, primefactors

def a019565(n): return reduce(mul, (prime(i+1) for i, v in enumerate(bin(n)[:1:-1]) if v == '1')) if n > 0 else 1 # This function from Chai Wah Wu

def a007947(n): return 1 if n<2 else reduce(mul, primefactors(n))

def a065642(n):

    if n==1: return 1

    r=a007947(n)

    n = n + r

    while a007947(n)!=r:

        n+=r

    return n

def A(n, k): return a019565(k) if n==1 else a065642(A(n - 1, k))

for n in range(1, 11): print([A(k, n - k + 1) for k in range(1, n + 1)]) # Indranil Ghosh, Apr 18 2017

CROSSREFS

Transpose: A285322.

Cf. A019565, A065642.

Cf. A008479 (index of the row where n is located), A087207 (of the column).

Cf. arrays A284311, A285325, also A285332.

Sequence in context: A207826 A035312 A056230 * A253561 A119919 A036561

Adjacent sequences:  A285318 A285319 A285320 * A285322 A285323 A285324

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, Apr 17 2017

STATUS

approved

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Last modified July 27 21:21 EDT 2021. Contains 346316 sequences. (Running on oeis4.)