A247073 - OEIS

%I #48 Nov 18 2014 15:04:49

%S 1,2,1,4,1,1,6,2,1,1,11,3,2,1,1,18,4,2,1,1,1,31,5,3,2,1,1,1,54,6,3,2,

%T 2,1,1,1,97,8,4,2,2,1,1,1,1,172,11,4,3,2,2,1,1,1,1,309,14,5,3,2,2,1,1,

%U 1,1,1,564,18,6,4,3,2,2,1,1,1,1,1,1028,24,8,4,3,2,2,2,1,1,1,1,1

%N Triangle read by rows: T(n,k) is the number of k-th prime powers up to 2^n, for k = 1 to n.

%H Reinhard Zumkeller, <a href="/A247073/b247073.txt">Rows n = 1..20 of triangle, flattened</a>

%e Up to 16, there are 6 primes (2, 3, 5, 7, 11, 13), 2 squared primes (4,9), 1 cube (8), and 1 fourth power (16), so 4th row is 6, 2, 1, 1.

%e Triangle starts:

%e 1;

%e 2, 1;

%e 4, 1, 1;

%e 6, 2, 1, 1;

%e 11, 3, 2, 1, 1;

%e 18, 4, 2, 1, 1, 1;

%e ...

%o (PARI) tabl(nn) = {for (n=1, nn, v = vector(2^n, i, i); vr = vector(n); for (k=1, #v, if (pp = isprimepower(v[k]), vr[pp] ++);); for (k=1, n, print1(vr[k], ", ");); print(););}

%o (Haskell)

%o import Data.List (sort, groupBy); import Data.Function (on)

%o a247073 n k = a247073_tabl !! (n-1) !! (k-1)

%o a247073_tabl = map a247073_row [1..]

%o a247073_row n = map length $ groupBy ((==) `on` fst) $ sort $

%o    takeWhile ((<= 2^n). snd) $ tail $ zip a025474_list a000961_list

%o -- _Reinhard Zumkeller_, Nov 18 2014

%Y Cf. A000961 (prime powers), A007053 (first column), A060967 (second column).

%Y Cf. A025474.

%K nonn,tabl

%O 1,2

%A _Michel Marcus_, Nov 18 2014