A347167 Numbers k such that phi(binomial(k,2)) is a power of 2.

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

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, Springer-Verlag, New York, 2001, p. 86.

F. Luca, Pascal's triangle and constructible polygons, Util. Math. 58 (2000d), pp. 209-214.

Links

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

Formula

For n >= 13, a(n) = A019434(n-7) (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