

A347167


Numbers k such that phi(binomial(k,2)) is a power of 2.


0



2, 3, 4, 5, 6, 16, 17, 256, 257, 65536, 65537, 4294967296
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OFFSET

1,1


COMMENTS

Every Fermat prime appears in this sequence.
A number greater than 2^32 is in this sequence if and only if it is a Fermat prime.


REFERENCES

M. Krizek, F. Luca and L. Somer, 17 Lectures on Fermat Numbers: From Number Theory to Geometry, CMS Books in Mathematics, vol. 9, SpringerVerlag, New York, 2001, p. 86.
F. Luca, Pascal's triangle and constructible polygons, Util. Math. 58 (2000d), pp. 209214.


LINKS

Table of n, a(n) for n=1..12.


FORMULA

For n >= 13, a(n) = A019434(n7) (if it exists).


MATHEMATICA

Select[Range[10^5], IntegerQ@Log2[EulerPhi@Binomial[#, 2]]&] (* Giorgos Kalogeropoulos, Sep 08 2021 *)


PROG

(Magma) r:=7; IsInteger:=func<i  i eq Floor(i)>; lst:=[k: k in [2..6]  IsInteger(Log(2, EulerPhi(Binomial(k, 2))))]; t:=1; for x in [1..r] do m:=4^(2^x); if t eq 1 then Append(~lst, m); end if; if IsPrime(m+1) then Append(~lst, m+1); else t:=0; end if; end for; lst;


CROSSREFS

Cf. A019434, A086700.
Sequence in context: A037341 A228730 A062932 * A166098 A124365 A115896
Adjacent sequences: A347164 A347165 A347166 * A347168 A347169 A347170


KEYWORD

nonn,hard,more


AUTHOR

Arkadiusz Wesolowski, Aug 20 2021


STATUS

approved



