A248906 Binary representation of prime power divisors of n: sum(p^k | n, 2^(A065515(p^k)-1)).

0, 1, 2, 5, 8, 3, 16, 37, 66, 9, 128, 7, 256, 17, 10, 549, 1024, 67, 2048, 13, 18, 129, 4096, 39, 8200, 257, 16450, 21, 32768, 11, 65536, 131621, 130, 1025, 24, 71, 262144, 2049, 258, 45, 524288, 19, 1048576, 133, 74, 4097, 2097152, 551, 4194320, 8201

Offset

1,3

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

Additive with a(p^k) = sum(j=1,k,2^(A065515(p^j)-1).

a(A051451(k)) = 2^k - 1.

a(n) = sum(2^(A095874(A210208(n,k))-2): k = 1..A073093(n)). - Reinhard Zumkeller, Mar 07 2015

Example

The prime power divisors of 12 are 2, 3, and 4. These are indices 1, 2, and 3 in the list of prime powers, so a(12) = 2^(1-1) + 2^(2-1) + 2^(3-1) = 7.

Prog

(PARI) al(n) = my(r=vector(n), pps=[p| p <- [1..n], isprimepower(p)], p2); for(k=1, #pps, p2=2^(k-1); forstep(j=pps[k], n, pps[k], r[j]+=p2)); r
(Haskell)
a248906 = sum . map ((2 ^) . subtract 2 . a095874) . tail . a210208_row
-- Reinhard Zumkeller, Mar 07 2015

Crossrefs

Cf. A246655, A065515, A034729, A000961.

Cf. A095874, a210208, A073093, A000079.

Sequence in context: A021391 A162611 A152248 * A075175 A075173 A163337

Adjacent sequences: A248903 A248904 A248905 * A248907 A248908 A248909

Keyword

nonn

Author

Franklin T. Adams-Watters, Mar 06 2015

Status

approved