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Triangle read by rows: row n contains the first n+1 numbers m such that A046660(m) = n.
13

%I #47 Sep 17 2021 16:50:22

%S 1,4,9,8,24,27,16,48,72,80,32,96,144,160,216,64,192,288,320,432,448,

%T 128,384,576,640,864,896,1296,256,768,1152,1280,1728,1792,2592,2816,

%U 512,1536,2304,2560,3456,3584,5184,5632,6400,1024,3072,4608,5120,6912,7168,10368,11264,12800,13312

%N Triangle read by rows: row n contains the first n+1 numbers m such that A046660(m) = n.

%C At the suggestion of _Michel Marcus_'s remark in _Carlos Eduardo Olivieri_'s A261256.

%H Reinhard Zumkeller, <a href="/A257851/b257851.txt">Rows n = 0..20 of triangle, flattened</a>

%F T(n,0) = A151821(n+1);

%F T(n,n-1) = A261256(n) for n > 0;

%F T(n,n) = A264959(n).

%F T(0,0) = A005117(1);

%F T(1,k) = A060687(k+1), k = 0..1;

%F T(2,k) = A195086(k+1), k = 0..2;

%F T(3,k) = A195087(k+1), k = 0..3;

%F T(4,k) = A195088(k+1), k = 0..4;

%F T(5,k) = A195089(k+1), k = 0..5;

%F T(6,k) = A195090(k+1), k = 0..6;

%F T(7,k) = A195091(k+1), k = 0..7;

%F T(8,k) = A195092(k+1), k = 0..8;

%F T(9,k) = A195093(k+1), k = 0..9;

%F T(10,k) = A195069(k+1), k = 0..10.

%e 0: 1

%e 1: 4 9

%e 2: 8 24 27

%e 3: 16 48 72 80

%e 4: 32 96 144 160 216

%e 5: 64 192 288 320 432 448

%e 6: 128 384 576 640 864 896 1296

%e 7: 256 768 1152 1280 1728 1792 2592 2816

%e 8: 512 1536 2304 2560 3456 3584 5184 5632 6400

%e -- ------------------------------------------------------------

%e 0: 1

%e 1: 2^2 3^2

%e 2: 2^3 2^3*3 3^3

%e 3: 2^4 2^4*3 2^3*3^2 2^4*5

%e 4: 2^5 2^5*3 2^4*3^2 2^5*5 2^3*3^3

%e 5: 2^6 2^6*3 2^5*3^2 2^6*5 2^4*3^3 2^6*7

%e 6: 2^7 2^7*3 2^6*3^2 2^7*5 2^5*3^3 2^7*7 2^4*3^4

%e 7: 2^8 2^8*3 2^7*3^2 2^8*5 2^6*3^3 2^8*7 2^5*3^4 2^8*11

%e 8: 2^9 2^9*3 2^8*3^2 2^9*5 2^7*3^3 2^9*7 2^6*3^4 2^9*11 2^8*5^2

%t T[n_] := Reap[For[m = 1; k = 1, k <= n+1, If[PrimeOmega[m] - PrimeNu[m] == n, Sow[m]; k++]; m++]][[2, 1]];

%t Table[T[n], {n, 0, 10}] // Flatten (* _Jean-François Alcover_, Sep 17 2021 *)

%o (Haskell)

%o a257851 n k = a257851_tabl !! n !! k

%o a257851_row n = a257851_tabl !! n

%o a257851_tabl = map

%o (\x -> take (x + 1) $ filter ((== x) . a046660) [1..]) [0..]

%Y Cf. A046660, A151821, A261256.

%Y Cf. A005117, A060687, A195086, A195087, A195088, A195089, A195090, A195091, A195092, A195093, A195069.

%K nonn,tabl

%O 0,2

%A _Reinhard Zumkeller_, Nov 29 2015