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URL: https://oeis.org/A143026

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A143026
Positive integers k such that the fourth power of the number of positive divisors of k equals k.
1
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.
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
Sequence in context: A046755 A016816 A046756 * A238700 A064781 A372845
KEYWORD
fini,nonn,full
AUTHOR
Emeric Deutsch, Aug 11 2008
EXTENSIONS
Second reference added by Harvey P. Dale, Oct 17 2011
STATUS
approved