# [seqfan] Artur (by way of O. Gérard) Help Needed for factorization

Olivier Gerard olivier.gerard at gmail.com
Thu Nov 20 17:25:41 CET 2008

```Dear Jack,

Could you confirm my conjecture that the number of prime divisors of numbers
(2^EulerPhi[3^n] - 1)/3^n is 0,1 or a prime number

a(n)=0, 0, 1, 3, 5, 11, 19

because you have good algorithmm for finding small divisors, you may be able to
find total number for some n>7

Mathematica tried factoring on my machine

1330560206356479874437581808691225710711634173623638361001698161624807\
9279126427105233053103284238007262282978961283301626482919922623957738\
2611453884961785422078720891479787457044659989325136247370735966256412\
9863013583118913903182578923381081567912635533663584632871383920445968\
5713267042987

for three days.

I have written a procedure to extract relatively quickly "small"
divisors and now I have to factor

1966382802018295849983426140507775310581529713937897353137000391612422\
8278817175390596880190641015445045632436171849324612595906231468275752\
7061637282120947925875224843503921645170678491988278295011723585321614\
64349494218512454182166238160960541165661049938151951871347

and the next prime divisor should be of the form 486 k + 1 and k>1000001

And a general question to all seqfans:
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someone sent on the list about one year ago a link to a server where I