

A058627


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


4



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



