A252997 Numbers n such that sigma(x) - x = n has at least two solutions, with each x having the same squarefree kernel, where sigma(x) is the sum of divisor function (A000203).

218, 189648, 720240, 119967120, 129705984, 517941905, 707902440, 1321744320, 98890370304, 99080219520, 119922568640, 139834382688, 347612467648, 580542318720, 952717920000, 1064902900320, 1153644808680, 2255573174400, 3903820736256, 6859688278905, 10944640212480, 14424196864000

Offset: 1

Author

Naohiro Nomoto, Dec 25 2014

Keywords

• nonn

Comments

Numbers n such that n = A001065(j) = A001065(k) and A007947(j) = A007947(k), where j != k.

Examples

			218 is the sum of proper divisors of 250 and 160, and rad(250) = rad(160) = 10, hence 218 is in the sequence with j=250 and k=160.
Other examples of n and j, k:
For n = 189648, j = 95832, k = 85536.
For n = 720240, j = 288120, k = 246960.
For n = 119967120, j = 38755080, k = 34398000.
For n = 129705984, j = 71614464, k = 60424704.
		

Links

• Carlos Rivera, Prime Puzzle 774. S(i) and Rad(i), The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A001065 (sum of proper divisors of n), A007947 (squarefree kernel of n).

Cf. A048138, A152454, A254035.

Extensions

a(6) onward from Fred Schneider, Feb 07 2015