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 A221645 Square array read by antidiagonals: T(n,k^2) = A040000(n) (= 1,2,2,2,...) if n=0 (mod k), T(n,k) = 0 else, n>=0, k>=1. 5
 1, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Other definition: Square array read by antidiagonal: T(n,k), n>=0, k>=1, in which column k lists the numbers A040000 (1, 2, 2, 2, 2...) interleaved with k^(1/2)-1 zeros, if k is a square otherwise column k lists only zeros. The sum of elements of the n-th antidiagonal equals the number of divisors of n. In other words, the antidiagonal sums give A000005. LINKS Table of n, a(n) for n=1..91. FORMULA sum_{k=1...n} a(n-k,k) = A000005(n) for all n>0. - M. F. Hasler, Feb 02 2013 EXAMPLE First 16 elements of first 16 rows of the square array are 1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,... 2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,... 2,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,... 2,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,... 2,0,0,2,0,0,0,0,0,0,0,0,0,0,0,2,... 2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,... 2,0,0,2,0,0,0,0,2,0,0,0,0,0,0,0,... 2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,... 2,0,0,2,0,0,0,0,0,0,0,0,0,0,0,2,... 2,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,... 2,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,... 2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,... 2,0,0,2,0,0,0,0,2,0,0,0,0,0,0,2,... 2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,... 2,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,... 2,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,... ... For n = 3 the sum of the third antidiagonal is 2+0+0 = d(3) = A000005(3) = 2. For n = 16 the sum of the 16th antidiagonal is 2+0+0+2+0+0+0+0+0+0+0+0+0+0+0+1 = d(16) = A000005(16) = 5. PROG (PARI) A221645(n, m)={my(t); issquare(m, &t)||return; n||return(1); n%t & return; 2} \\ M. F. Hasler, Feb 02 2013 CROSSREFS Cf. A000005, A212119. Sequence in context: A227618 A366533 A340683 * A216176 A359007 A128765 Adjacent sequences: A221642 A221643 A221644 * A221646 A221647 A221648 KEYWORD nonn,tabl AUTHOR Omar E. Pol, Feb 02 2013 STATUS approved

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Last modified September 15 08:13 EDT 2024. Contains 375932 sequences. (Running on oeis4.)