A289056 Near 3-perfect numbers of the form 2^a*p^t*q, where a >= 1, t = 1 or 2, p < q are both primes.

180, 240, 360, 1344, 1872, 2688, 3744, 5376, 6048, 6496

Offset: 1

Author

Vladimir Shevelev, Jun 23 2017

Keywords

• nonn
• fini
• full

Comments

A positive number m is called a near perfect number if the sum of its divisors (A000203) is 3*m+d, where d is a proper divisor of m. Recently [Das and Saikia] proved that there exist only 10 such numbers with the restriction in the name.

Examples

			For m=240, d=24, A000203(m) = 744 = 3*240 + d. So 240 is a member.
		

Links

• B. Das and H. K. Saikia, On near 3-perfect numbers, Sohag Journal of Math., Vol. 4, No. 1 (2017), 1-5.
• Paul Pollack and Vladimir Shevelev, On perfect and near-perfect numbers, J. Number Theory 132 (2012), pp. 3037-3046.

Crossrefs

Cf. A000203, A181595.