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

1,1

Comments

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

Links

Table of n, a(n) for n=1..22.

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

Example

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.

Crossrefs

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

Cf. A048138, A152454, A254035.

Sequence in context: A209824 A230333 A060530 * A126829 A171406 A025406

Adjacent sequences: A252994 A252995 A252996 * A252998 A252999 A253000

Keyword

nonn

Author

Naohiro Nomoto, Dec 25 2014

Extensions

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

Status

approved