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A285325 Square array A(n,k) = A048675(A285321(n,k)), read by descending antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ... 6
1, 2, 2, 3, 4, 3, 4, 4, 6, 4, 5, 8, 5, 8, 5, 6, 6, 12, 5, 10, 6, 7, 8, 7, 16, 6, 12, 7, 8, 8, 10, 9, 20, 6, 14, 8, 9, 16, 9, 10, 8, 24, 7, 16, 9, 10, 10, 24, 9, 12, 10, 28, 7, 18, 10, 11, 12, 11, 32, 11, 14, 9, 32, 7, 20, 11, 12, 12, 18, 17, 40, 10, 12, 11, 36, 8, 22, 12, 13, 16, 13, 14, 12, 48, 10, 14, 13, 40, 8, 24, 13 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

A(n,k) = A048675(A285321(n,k)).

EXAMPLE

The top left 15x6 corner of the array:

  1,  2, 3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15

  2,  4, 4,  8,  6,  8,  8, 16, 10, 12, 12, 16, 14, 16, 16

  3,  6, 5, 12,  7, 10,  9, 24, 11, 18, 13, 20, 15, 18, 17

  4,  8, 5, 16,  9, 10,  9, 32, 17, 14, 13, 20, 17, 22, 17

  5, 10, 6, 20,  8, 12, 11, 40, 12, 20, 14, 24, 21, 18, 19

  6, 12, 6, 24, 10, 14, 10, 48, 18, 16, 19, 28, 16, 20, 18

PROG

(PARI)

A019565(n) = {my(j, v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ This function from M. F. Hasler

A007947(n) = factorback(factorint(n)[, 1]); \\ From Andrew Lelechenko, May 09 2014

A065642(n) = { my(r=A007947(n)); if(1==n, n, n = n+r; while(A007947(n) <> r, n = n+r); n); };

A285321bi(row, col) = if(1==row, A019565(col), A065642(A285321bi(row-1, col)));

A002260(n)= { n-binomial((sqrtint(8*n)+1)\2, 2); }; \\ M. F. Hasler, Mar 10 2014

A004736(n)= { 1 + binomial(1 + floor(1/2 + sqrt(2*n)), 2) - n; };

A285321(n) = A285321bi(A002260(n), A004736(n));

A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; \\ Michel Marcus, Oct 10 2016

A285325(n) = A048675(A285321(n));

for(n=1, 120, write("b285325.txt", n, " ", A285325(n)));

(Scheme)

(define (A285325 n) (A285325bi (A002260 n) (A004736 n)))

(define (A285325bi row col) (A048675 (A285321bi row col)))

CROSSREFS

Cf. A048675, A285321, A285333.

Row 1 & column 1: A000027.

Row 2: A285326, Row 3: A285327.

Sequence in context: A081742 A127432 A199408 * A135529 A061282 A244040

Adjacent sequences:  A285322 A285323 A285324 * A285326 A285327 A285328

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, Apr 17 2017

STATUS

approved

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Last modified June 25 07:18 EDT 2019. Contains 324347 sequences. (Running on oeis4.)