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 A077609 Triangle in which n-th row lists infinitary divisors of n. 23
 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 2, 3, 6, 1, 7, 1, 2, 4, 8, 1, 9, 1, 2, 5, 10, 1, 11, 1, 3, 4, 12, 1, 13, 1, 2, 7, 14, 1, 3, 5, 15, 1, 16, 1, 17, 1, 2, 9, 18, 1, 19, 1, 4, 5, 20, 1, 3, 7, 21, 1, 2, 11, 22, 1, 23, 1, 2, 3, 4, 6, 8, 12, 24, 1, 25, 1, 2, 13, 26, 1, 3, 9, 27, 1, 4, 7, 28, 1, 29, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Reinhard Zumkeller, Rows n = 1..1000 of table, flattened G. L. Cohen, P. Hagis, Jr, Arithmetic functions associated with the infinitary divisors of an integer, Internat. J. Math. Math. Sci. 16 (2) (1993) 373-384 Eric Weisstein's World of Mathematics, Infinitary Divisor EXAMPLE The first few rows are: 1; 1, 2; 1, 3; 1, 4; 1, 5; 1, 2, 3, 6; 1, 7; 1, 2, 4, 8; 1, 9; 1, 2, 5, 10; 1, 11; 1, 3, 4, 12; MAPLE # see the function idivisors() in A049417. # R. J. Mathar, Oct 05 2017 MATHEMATICA f[x_] := If[x == 1, 1, Sort@ Flatten@ Outer[Times, Sequence @@ (FactorInteger[x] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]] ; Array[f, 30] // Flatten (* Paul Abbott (paul(AT)physics.uwa.edu.au), Apr 29 2005 *) (* edited by Michael De Vlieger, Jun 07 2016 *) PROG (Haskell) import Data.List ((\\)) a077609 n k = a077609_row n !! (k-1) a077609_row n = filter    (\d -> d == 1 || null (a213925_row d \\ a213925_row n)) \$ a027750_row n a077609_tabf = map a077609_row [1..] -- Reinhard Zumkeller, Jul 10 2013 (PARI) isidiv(d, f) = {if (d==1, return (1)); for (k=1, #f~, bne = binary(f[k, 2]); bde = binary(valuation(d, f[k, 1])); if (#bde < #bne, bde = concat(vector(#bne-#bde), bde)); for (j=1, #bne, if (! bne[j] && bde[j], return (0)); ); ); return (1); } row(n) = {d = divisors(n); f = factor(n); idiv = []; for (k=1, #d, if (isidiv(d[k], f), idiv = concat(idiv, d[k])); ); idiv; } \\ Michel Marcus, Feb 15 2016 CROSSREFS Cf. A027750, A037445, A049417 (row sums). Sequence in context: A180184 A330752 A222266 * A077610 A329534 A317746 Adjacent sequences:  A077606 A077607 A077608 * A077610 A077611 A077612 KEYWORD nonn,tabf AUTHOR Eric W. Weisstein, Nov 11 2002 STATUS approved

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Last modified August 5 03:00 EDT 2021. Contains 346457 sequences. (Running on oeis4.)