A257851 Triangle read by rows: row n contains the first n+1 numbers m such that A046660(m) = n.

1, 4, 9, 8, 24, 27, 16, 48, 72, 80, 32, 96, 144, 160, 216, 64, 192, 288, 320, 432, 448, 128, 384, 576, 640, 864, 896, 1296, 256, 768, 1152, 1280, 1728, 1792, 2592, 2816, 512, 1536, 2304, 2560, 3456, 3584, 5184, 5632, 6400, 1024, 3072, 4608, 5120, 6912, 7168, 10368, 11264, 12800, 13312

Offset: 0

Author

Reinhard Zumkeller, Nov 29 2015

Keywords

• nonn
• tabl

Comments

At the suggestion of Michel Marcus's remark in Carlos Eduardo Olivieri's A261256.

Examples

			0:    1
1:    4     9
2:    8    24      27
3:   16    48      72    80
4:   32    96     144   160     216
5:   64   192     288   320     432   448
6:  128   384     576   640     864   896    1296
7:  256   768    1152  1280    1728  1792    2592   2816
8:  512  1536    2304  2560    3456  3584    5184   5632    6400
--  ------------------------------------------------------------
0:  1
1:  2^2   3^2
2:  2^3 2^3*3     3^3
3:  2^4 2^4*3 2^3*3^2 2^4*5
4:  2^5 2^5*3 2^4*3^2 2^5*5 2^3*3^3
5:  2^6 2^6*3 2^5*3^2 2^6*5 2^4*3^3 2^6*7
6:  2^7 2^7*3 2^6*3^2 2^7*5 2^5*3^3 2^7*7 2^4*3^4
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
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
		

Links

• Reinhard Zumkeller, Rows n = 0..20 of triangle, flattened

Crossrefs

Cf. A046660, A151821, A261256.

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

Programs

Haskell

a257851 n k = a257851_tabl !! n !! k
a257851_row n = a257851_tabl !! n
a257851_tabl = map
   (\x -> take (x + 1) $ filter ((== x) . a046660) [1..]) [0..]

Mathematica

T[n_] := Reap[For[m = 1; k = 1, k <= n+1, If[PrimeOmega[m] - PrimeNu[m] == n, Sow[m]; k++]; m++]][[2, 1]];
Table[T[n], {n, 0, 10}] // Flatten (* Jean-François Alcover, Sep 17 2021 *)

Formula

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

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

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

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

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

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

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

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

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

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

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

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

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

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