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.

A318875 Number of divisors d of n for which 2*phi(d) < d.

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%I A318875 #13 Jul 08 2024 10:40:57
%S A318875 0,0,0,0,0,1,0,0,0,1,0,2,0,1,0,0,0,2,0,2,0,1,0,3,0,1,0,2,0,3,0,0,0,1,
%T A318875 0,4,0,1,0,3,0,3,0,2,0,1,0,4,0,2,0,2,0,3,0,3,0,1,0,6,0,1,0,0,0,3,0,2,
%U A318875 0,3,0,6,0,1,0,2,0,3,0,4,0,1,0,6,0,1,0,3,0,5,0,2,0,1,0,5,0,2,0,4,0,3,0,3,1
%N A318875 Number of divisors d of n for which 2*phi(d) < d.
%H A318875 Antti Karttunen, <a href="/A318875/b318875.txt">Table of n, a(n) for n = 1..65537</a>
%F A318875 a(n) = Sum_{d|n} [A083254(d) < 0].
%F A318875 For all n >= 1, a(n) + A318874(n) + A007814(n) = A000005(n).
%p A318875 A318875 := n -> nops(select(d -> (2*numtheory:-phi(d)) < d, divisors(n))):
%p A318875 seq(A318875(n), n=1..199); # _Peter Luschny_, Sep 05 2018
%t A318875 A318875[n_] := DivisorSum[n, 1 &, 2*EulerPhi[#] < # &];
%t A318875 Array[A318875, 100] (* _Paolo Xausa_, Jul 08 2024 *)
%o A318875 (PARI) A318875(n) = sumdiv(n,d,(2*eulerphi(d))<d);
%Y A318875 Cf. A000010, A083254, A318874, A318877, A318879.
%K A318875 nonn
%O A318875 1,12
%A A318875 _Antti Karttunen_, Sep 05 2018