A114887 Multiperfect numbers sigma(n) = k*n, which are divisible by the sum of their prime factors without repetition.

120, 672, 32760, 2178540, 1379454720, 14182439040, 518666803200, 30823866178560, 71065075104190073088, 154345556085770649600, 9186050031556349952000, 680489641226538823680000

Offset: 1

Author

Sven Simon, Feb 19 2006

Keywords

• nonn

Comments

From a list of about 5000 multiperfect numbers, 38 numbers were found with the property, all having k <= 9, the largest was the only one having k=9. A091443 uses sopfr with repetition.

Conjecture: the sequence is finite.

Examples

			a(0) = 120 = 2^3*3*5, sopf(120) = 2+3+5 = 10.
		

Links

• Sven Simon, Table of n, a(n) for n = 1..38 [Conjectured to be complete]
• Achim Flammenkamp, The Multiply Perfect Numbers Page (See here for the latest information about the search)
• Eric Weisstein's World of Mathematics, Multiperfect numbers

Crossrefs

Cf. A091443.

Intersection of A007691 and A089352. - Michel Marcus, Oct 08 2017