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A107655
a(n) is the smallest number m greater than 1 such that phi(m) = d(m)^n, where d(m) is number of positive divisors of m; if there is no such m, a(n)=1.
5
3, 5, 85, 17, 1285, 4369, 559876, 257, 327685, 1114129, 1114521441417, 16843009, 160490068541289, 1925878801139721, 23110536763219977, 65537, 3327917287071744009, 39934999967815157769, 479219999336720898057, 5750639996603165650953, 69007679885506346588169, 828092158571811231498249, 9937105900443065378930697
OFFSET
1,1
COMMENTS
For n=0,1,2,3, and 4, a(2^n) = A000215(n), the n-th Fermat prime.
Conjecture: A000005(a(n)) <= 12 for all n. [Max Alekseyev, May 07 2010]
This conjecture holds throughout the first 102 terms. - David A. Corneth, Jun 14 2020
LINKS
Max Alekseyev, PARI scripts for various problems (see invphitau there).
EXAMPLE
a(10) = 1114129 because phi(1114129) = d(1114129)^10 and 1114129 is the smallest number m greater than 1 that phi(m) = 1048576 = 4^10 = d(m)^10.
PROG
(PARI) a(n)=res = oo; for(i=2, oo, if(i^n > res, return(res)); c=invphitau(i^n, i); if(#c>0, res=c[1])) \\ for invphitau, see Alekseyev link \\ David A. Corneth, Jun 14 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Farideh Firoozbakht, Jun 06 2005
EXTENSIONS
Terms a(11) onward from Max Alekseyev, May 07 2010
Terms a(20)-a(23), offset corrected by David A. Corneth, Jun 14 2020
STATUS
approved