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

1, 625, 6561, 4100625

Offset

1,2

Comments

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

There are no more terms in the sequence.

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.

Links

Table of n, a(n) for n=1..4.

Example

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

Mathematica

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

Crossrefs

Cf. A066693, A180936.

Sequence in context: A046755 A016816 A046756 * A238700 A064781 A250832

Adjacent sequences: A143023 A143024 A143025 * A143027 A143028 A143029

Keyword

fini,nonn,full

Author

Emeric Deutsch, Aug 11 2008

Extensions

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

Status

approved