A175837 -id:A175837 - cp's OEIS frontend

A175853 (2*n-1)-perfect numbers.

20, 128768, 33501184

Offset: 1

Vladimir Shevelev, Dec 05 2010

For the definition see A175837.

Considering only terms of the form 2^k * p with p prime results in a linear equation for p for a given k. Solving quickly generates other terms of the sequence: 137433972736, 2199001235456, 649037107316852462774394019643392, and a 157-digit term associated with k=260. - D. S. McNeil, Dec 08 2010

			Proper divisors of 20 are: 1,2,4,5,10. Since 2*20-1=(2*1-1)+(2*2-1)+(2*4-1)+(2*5-1)+(2*10-1)=39, then 20 is in the sequence.

Cf. A175837 (abundant version), A175522, A033880, A000005.

A033880(a(n))=A000005(a(n))/2-1.

a(3) from D. S. McNeil, Dec 08 2010

A177085 Ceiling(n/3)-abundant numbers.

Original entry on oeis.org

6, 8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 44, 48, 54, 56, 60, 64, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 110, 112, 114, 120, 126, 128, 132, 136, 138, 140, 144, 150, 152, 156, 160, 162, 168, 174, 176, 180, 186, 192, 196, 198, 200

Offset: 1

Vladimir Shevelev, Dec 09 2010

nonn

For definition, see comment to A175522.

It appears most terms are even, but there exist odd terms: 945, 1155, 1575, etc. For n < 10^5 there are 211 odd terms of the sequence and 24628 even ones.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A177084 (perfect version), A005100, A005101, A175524, A175526, A175811, A175821, A175837, A074206, A177052.

isok(n) = sumdiv(n, d, (d ceil(n/3); \\ Michel Marcus, Feb 08 2016

is_A177085 = lambda n: sum(ceil(d/3) for d in divisors(n)) > 2*ceil(n/3) # D. S. McNeil, Dec 10 2010

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A175853 (2*n-1)-perfect numbers.

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A177085 Ceiling(n/3)-abundant numbers.

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