

A099069


Numbers n such that n = prime(d_1*d_2*...*d_k)  phi(d_1 + d_2 + ... + d_k) where d_1 d_2 ... d_k is the decimal expansion of n.


2




OFFSET

1,2


COMMENTS

Sequence is finite since prime(d_1*d_2*...*d_k) <= prime(9^k) <= 9^k(k log 9 + log k + log log 9) < 10^(k1) for large enough k, i.e., it will have fewer than k digits. In particular, a(n) < 10^69.  Chai Wah Wu, Aug 10 2017


LINKS

Table of n, a(n) for n=1..5.
C. Rivera, Puzzle 279The Prime Puzzles & Problems connection.


EXAMPLE

35497 is in the sequence because 35497 = prime(3*5*4*9*7)  phi(3 + 5 + 4 + 9 + 7).


MATHEMATICA

Do[h=IntegerDigits[n]; l=Length[h]; If[ !MemberQ[h, 0]&&n==Prime[Product[h[[k]], {k, l}]]EulerPhi[Sum[h[[k]], {k, l}]], Print[n]], {n, 6000000}]


CROSSREFS

Cf. A097223, A097227, A099067, A099068.
Sequence in context: A066735 A232498 A254380 * A038584 A108022 A108884
Adjacent sequences: A099066 A099067 A099068 * A099070 A099071 A099072


KEYWORD

base,more,nonn,fini


AUTHOR

Farideh Firoozbakht, Oct 29 2004


STATUS

approved



