cp's OEIS Frontend

A247073 Triangle read by rows: T(n,k) is the number of k-th prime powers up to 2^n, for k = 1 to n.

%I A247073 #48 Nov 18 2014 15:04:49
%S A247073 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 A247073 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 A247073 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 A247073 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 A247073 Reinhard Zumkeller, <a href="/A247073/b247073.txt">Rows n = 1..20 of triangle, flattened</a>
%e A247073 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 A247073 Triangle starts:
%e A247073 1;
%e A247073 2, 1;
%e A247073 4, 1, 1;
%e A247073 6, 2, 1, 1;
%e A247073 11, 3, 2, 1, 1;
%e A247073 18, 4, 2, 1, 1, 1;
%e A247073 ...
%o A247073 (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 A247073 (Haskell)
%o A247073 import Data.List (sort, groupBy); import Data.Function (on)
%o A247073 a247073 n k = a247073_tabl !! (n-1) !! (k-1)
%o A247073 a247073_tabl = map a247073_row [1..]
%o A247073 a247073_row n = map length $ groupBy ((==) `on` fst) $ sort $
%o A247073    takeWhile ((<= 2^n). snd) $ tail $ zip a025474_list a000961_list
%o A247073 -- _Reinhard Zumkeller_, Nov 18 2014
%Y A247073 Cf. A000961 (prime powers), A007053 (first column), A060967 (second column).
%Y A247073 Cf. A025474.
%K A247073 nonn,tabl
%O A247073 1,2
%A A247073 _Michel Marcus_, Nov 18 2014