cp's OEIS Frontend

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

%I A248906 #17 Jul 11 2024 05:28:50
%S A248906 0,1,2,5,8,3,16,37,66,9,128,7,256,17,10,549,1024,67,2048,13,18,129,
%T A248906 4096,39,8200,257,16450,21,32768,11,65536,131621,130,1025,24,71,
%U A248906 262144,2049,258,45,524288,19,1048576,133,74,4097,2097152,551,4194320,8201
%N A248906 Binary representation of prime power divisors of n: Sum_{p^k | n} 2^(A065515(p^k)-1).
%H A248906 Reinhard Zumkeller, <a href="/A248906/b248906.txt">Table of n, a(n) for n = 1..10000</a>
%F A248906 Additive with a(p^k) = Sum_{j=1..k} 2^(A065515(p^j)-1).
%F A248906 a(A051451(k)) = 2^k - 1.
%F A248906 a(n) = Sum_{k=1..A073093(n)} 2^(A095874(A210208(n,k))-2). - _Reinhard Zumkeller_, Mar 07 2015
%e A248906 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.
%o A248906 (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
%o A248906 (Haskell)
%o A248906 a248906 = sum . map ((2 ^) . subtract 2 . a095874) . tail . a210208_row
%o A248906 -- _Reinhard Zumkeller_, Mar 07 2015
%Y A248906 Cf. A246655, A065515, A034729, A000961.
%Y A248906 Cf. A095874, A210208, A073093, A000079.
%K A248906 nonn
%O A248906 1,3
%A A248906 _Franklin T. Adams-Watters_, Mar 06 2015