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URL: https://oeis.org/A248906

⇱ A248906 - OEIS

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A248906
Binary representation of prime power divisors of n: Sum_{p^k | n} 2^(A065515(p^k)-1).
2
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
FORMULA
Additive with a(p^k) = Sum_{j=1..k} 2^(A065515(p^j)-1).
a(A051451(k)) = 2^k - 1.
a(n) = Sum_{k=1..A073093(n)} 2^(A095874(A210208(n,k))-2). - 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
KEYWORD
nonn
AUTHOR
STATUS
approved