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 A177050 Ceiling(n/2)-perfect numbers. 4
 2, 4, 8, 10, 16, 32, 64, 110, 128, 136, 256, 512, 884, 1024, 2048, 4096, 8192, 16384, 18632, 32768, 32896, 65536, 70564, 100804, 116624, 131072, 262144, 391612, 449295, 524288, 1048576, 2097152, 4194304, 8388608, 15370304, 16777216, 33554432, 67108864, 73995392 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS Amiram Eldar, Table of n, a(n) for n = 1..47 PROG (Sage) is_A177050 = lambda n: sum(ceil(d/2) for d in divisors(n)) == 2*ceil(n/2) # D. S. McNeil, Dec 10 2010 (PARI) isok(n) = sumdiv(n, d, (d

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Last modified January 26 16:14 EST 2023. Contains 359833 sequences. (Running on oeis4.)