A058627 Numbers n such that phi(n) = product of the digits of n.

1, 24, 26, 87, 168, 388, 594, 666, 1998, 2688, 5698, 5978, 6786, 7888, 68796

Offset

1,2

Comments

Sequence is finite because for n large enough phi(n) > n / (exp(EulerGamma) * log(log(n))+3/log(log(n))), while pod(n) < 9*9^ceiling(log(n)/log(10)). If a(16) exists, it holds 10^13 < a(16) < 10^64. - Giovanni Resta, Apr 22 2014

References

C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Oxford University Press, NY 2000, Chapter 72, 'Apocalyptic Numbers,' Pages 176 - 178.

Links

Table of n, a(n) for n=1..15.

C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review

Example

Phi(666) = 6*6*6

Mathematica

Select[ Range[ 10^7], EulerPhi[ # ] == Times @@ IntegerDigits[ # ] &]

Crossrefs

Sequence in context: A295007 A053968 A336237 * A286130 A279427 A116203

Adjacent sequences: A058624 A058625 A058626 * A058628 A058629 A058630

Keyword

nonn,base,fini

Author

Robert G. Wilson v, Dec 26 2000

Status

approved