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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
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<n)*ceil(d/2)) == ceil(n/2); \\ Michel Marcus, Feb 08 2016
CROSSREFS
Sequence in context: A097210 A097214 A045579 * A276772 A173063 A066363
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Dec 09 2010
EXTENSIONS
a(31)-a(39) from Michel Marcus, Feb 08 2016
STATUS
approved

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Last modified May 29 04:26 EDT 2024. Contains 372921 sequences. (Running on oeis4.)