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.

A211778 Composite 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 A211778 #12 Jan 10 2025 02:02:12
%S A211778 8,12,32,80,81,128,189,196,324,336,448,512,576,768,1600,1936,2025,
%T A211778 2048,2187,2500,5292,5324,5616,5780,8192,8748,9477,11264,12096,13520,
%U A211778 14400,14800,15552,15625,20736,32768,35721,36864,49152,53248,59049,69696,73575,73872
%N A211778 Composite 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 A211778 Complement of primes (A000040) with respect to A211777.
%e A211778 For n = 32 holds: 1/1 + 1/2 + 2/4 + 4/8 + 8/16 = 3 (integer).
%t A211778 t = {}; Do[If[! PrimeQ[n], d2 = Sum[EulerPhi[d]/d, {d, Most[Divisors[n]]}]; If[IntegerQ[d2], AppendTo[t, n]]], {n, 2, 10000}]; t (* _T. D. Noe_, Apr 26 2012 *)
%o A211778 (PARI) is(n)=denominator(sumdiv(n, d, if(d<n, eulerphi(d)/d)))==1 && !isprime(n) \\ _Charles R Greathouse IV_, Mar 05 2013
%Y A211778 Cf. A066862 (numbers n such that Sum_{d | n} phi(d) / d is an integer).
%K A211778 nonn
%O A211778 1,1
%A A211778 _Jaroslav Krizek_, Apr 20 2012
%E A211778 Extended by _T. D. Noe_, Apr 26 2012