cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A211777 Numbers n such that Sum_{d_ phi(d_ is an integer, where d_ divisors of n that are less than n, phi(x) = A000010(x).

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%I A211777 #17 Jan 09 2025 13:20:07
%S A211777 2,3,5,7,8,11,12,13,17,19,23,29,31,32,37,41,43,47,53,59,61,67,71,73,
%T A211777 79,80,81,83,89,97,101,103,107,109,113,127,128,131,137,139,149,151,
%U A211777 157,163,167,173,179,181,189,191,193,196,197,199,211,223,227,229,233
%N A211777 Numbers n such that Sum_{d_<n | n} phi(d_<n) / (d_<n) is an integer, where d_<n = divisors of n that are less than n, phi(x) = A000010(x).
%C A211777 Union primes (A000040) and A211778.
%e A211777 For n = 32 holds: 1/1 + 1/2 + 2/4 + 4/8 + 8/16 = 3 (integer).
%t A211777 t = {}; Do[d2 = Sum[EulerPhi[d]/d, {d, Most[Divisors[n]]}]; If[IntegerQ[d2], AppendTo[t, n]], {n, 2, 233}]; t (* _T. D. Noe_, Apr 26 2012 *)
%o A211777 (PARI) is(n)=denominator(sumdiv(n,d,if(d<n,eulerphi(d)/d)))==1 \\ _Charles R Greathouse IV_, Feb 21 2013
%Y A211777 Cf: A066862 (numbers n such that Sum_{d | n} phi(d) / d is an integer).
%K A211777 nonn
%O A211777 1,1
%A A211777 _Jaroslav Krizek_, Apr 20 2012