A143026 Positive integers k such that the fourth power of the number of positive divisors of k equals k.

1, 625, 6561, 4100625

Offset: 1

Author

Emeric Deutsch, Aug 11 2008

Keywords

• fini
• nonn
• full

Comments

625=5^4, 6561=3^8, 4100625=(3^8)(5^4).

There are no more terms in the sequence.

Examples

			625 has 5 divisors (1, 5, 25, 125 and 625) and 5^4 = 625.
		

References

• T. Andreescu, D. Andrica and Z. Feng, 104 Number Theory Problems (from the training of the USA IMO team), Birkhäuser, Boston, 2007, Advanced problem # 19, pp. 85, 145, 146.
• Roozbeh Hazrat, Mathematica: A Problem-Centered Approach, Springer 2010, p. 39.

Crossrefs

Cf. A066693, A180936.

Programs

Mathematica

Select[Range[4200000],DivisorSigma[0,#]^4==#&] (* Harvey P. Dale, Oct 17 2011 *)

Extensions

Second reference added by Harvey P. Dale, Oct 17 2011