This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A177050 #25 Nov 17 2019 01:42:46 %S A177050 2,4,8,10,16,32,64,110,128,136,256,512,884,1024,2048,4096,8192,16384, %T A177050 18632,32768,32896,65536,70564,100804,116624,131072,262144,391612, %U A177050 449295,524288,1048576,2097152,4194304,8388608,15370304,16777216,33554432,67108864,73995392 %N A177050 Ceiling(n/2)-perfect numbers. %C A177050 All powers of 2 except for 1 are terms of the sequence. All numbers of the form 2^(2^k-1)*p, where p=2^(2^k)+1 is a Fermat prime (k >= 1) are in the sequence. Thus numbers 136, 32896, 2147516416 are in the sequence. It is interesting that in this construction Fermat primes play the same role that Mersenne primes in construction of usual even perfect numbers. Unfortunately, the conversion for even ceiling(n/2)-perfect numbers is false: the first counterexample, found by _D. S. McNeil_, is 110 = 2*5*11. Besides, the first odd term, found by _D. S. McNeil_, is 449295 = 3*5*7*11*389. %H A177050 Amiram Eldar, <a href="/A177050/b177050.txt">Table of n, a(n) for n = 1..47</a> %o A177050 (Sage) is_A177050 = lambda n: sum(ceil(d/2) for d in divisors(n)) == 2*ceil(n/2) # _D. S. McNeil_, Dec 10 2010 %o A177050 (PARI) isok(n) = sumdiv(n, d, (d<n)*ceil(d/2)) == ceil(n/2); \\ _Michel Marcus_, Feb 08 2016 %Y A177050 Cf. A000396, A175522, A175807, A175853. %K A177050 nonn %O A177050 1,1 %A A177050 _Vladimir Shevelev_, Dec 09 2010 %E A177050 a(31)-a(39) from _Michel Marcus_, Feb 08 2016