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A210208 Triangle read by rows in which row n lists the divisors of n that are prime powers, A000961.

%I A210208 #24 May 02 2025 03:31:55
%S A210208 1,1,2,1,3,1,2,4,1,5,1,2,3,1,7,1,2,4,8,1,3,9,1,2,5,1,11,1,2,3,4,1,13,
%T A210208 1,2,7,1,3,5,1,2,4,8,16,1,17,1,2,3,9,1,19,1,2,4,5,1,3,7,1,2,11,1,23,1,
%U A210208 2,3,4,8,1,5,25,1,2,13,1,3,9,27,1,2,4,7
%N A210208 Triangle read by rows in which row n lists the divisors of n that are prime powers, A000961.
%C A210208 {T(n,k): k = 1..A073093(n)} subset of {A027750(n,k): k = 1..A000005(n)} for all n.
%H A210208 Reinhard Zumkeller, <a href="/A210208/b210208.txt">Rows n=1..5000 of triangle, flattened</a>
%H A210208 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Divisor.html">Divisor</a>.
%F A210208 A034699(n) = T(n,A073093(n)) = maximum of n-th row.
%e A210208 Table begins:
%e A210208   1;
%e A210208   1, 2;
%e A210208   1, 3;
%e A210208   1, 2, 4;
%e A210208   1, 5;
%e A210208   1, 2, 3;
%e A210208   1, 7;
%e A210208   1, 2, 4, 8;
%e A210208   1, 3, 9;
%e A210208   1, 2, 5;
%e A210208   1, 11;
%e A210208   1, 2, 3, 4; - _Geoffrey Critzer_, Feb 08 2015
%t A210208 Table[Prepend[Select[Divisors[n], PrimeNu[#] == 1 &], 1], {n, 1, 10}]//Grid (* _Geoffrey Critzer_, Feb 08 2015 *)
%o A210208 (Haskell)
%o A210208 a210208 n k = a210208_tabf !! (n-1) !! (n-1)
%o A210208 a210208_row n = a210208_tabf !! (n-1)
%o A210208 a210208_tabf = map (filter ((== 1) . a010055)) a027750_tabf
%o A210208 (PARI) row(n) = select(x -> omega(x) < 2, divisors(n)); \\ _Amiram Eldar_, May 02 2025
%Y A210208 Cf. A073093 (row lengths), A023888 (row sums), A034699 (row maxima), A183091 (row products).
%Y A210208 Cf. A000005, A010055, A027750, A141809.
%K A210208 nonn,tabf
%O A210208 1,3
%A A210208 _Reinhard Zumkeller_, Mar 18 2012