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A107655
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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.
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5
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3, 5, 85, 17, 1285, 4369, 559876, 257, 327685, 1114129, 1114521441417, 16843009, 160490068541289, 1925878801139721, 23110536763219977, 65537, 3327917287071744009, 39934999967815157769, 479219999336720898057, 5750639996603165650953, 69007679885506346588169, 828092158571811231498249, 9937105900443065378930697
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OFFSET
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1,1
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COMMENTS
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For n=0,1,2,3, and 4, a(2^n) = A000215(n), the n-th Fermat prime.
This conjecture holds throughout the first 102 terms. - David A. Corneth, Jun 14 2020
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LINKS
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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