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), ...

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

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]); \\ 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