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.

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, 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, 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

Offset

1,2

Links

Reinhard Zumkeller, Rows n = 1..20 of triangle, flattened

Example

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.
Triangle starts:
1;
2, 1;
4, 1, 1;
6, 2, 1, 1;
11, 3, 2, 1, 1;
18, 4, 2, 1, 1, 1;
...

Prog

(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(); ); }
(Haskell)
import Data.List (sort, groupBy); import Data.Function (on)
a247073 n k = a247073_tabl !! (n-1) !! (k-1)
a247073_tabl = map a247073_row [1..]
a247073_row n = map length $ groupBy ((==) `on` fst) $ sort $
   takeWhile ((<= 2^n). snd) $ tail $ zip a025474_list a000961_list
-- Reinhard Zumkeller, Nov 18 2014

Crossrefs

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

Cf. A025474.

Sequence in context: A131034 A346873 A130313 * A124428 A191310 A124845

Adjacent sequences: A247070 A247071 A247072 * A247074 A247075 A247076

Keyword

nonn,tabl

Author

Michel Marcus, Nov 18 2014

Status

approved