cp's OEIS Frontend

A281687 Number of partitions of 2*n into the sum of two totient numbers (A002202).

%I A281687 #35 Feb 02 2017 08:58:09
%S A281687 1,1,1,2,2,3,3,3,3,4,4,5,5,5,5,6,6,6,6,7,6,7,7,9,8,9,8,9,9,11,10,12,
%T A281687 10,11,10,12,11,13,10,11,12,13,12,15,13,12,13,13,12,15,14,14,14,16,15,
%U A281687 19,16,16,16,17,15,19,15,18,16,19,16,20,18,19,18,20,17,22,19,21,18,21,19,22
%N A281687 Number of partitions of 2*n into the sum of two totient numbers (A002202).
%C A281687 See also graph of A045917 ("Goldbach's comet"). - _Altug Alkan_, Jan 30 2017
%H A281687 Robert Israel, <a href="/A281687/b281687.txt">Table of n, a(n) for n = 1..10000</a>
%H A281687 Altug Alkan, <a href="/A281687/a281687.png">Illustration Of Residue Classes Modulo 6</a>
%e A281687 a(6) = 3 because 2 * 6 = 12 = 2 + 10 = 4 + 8 = 6 + 6 and 2, 4, 6, 8, 10 are in A002202.
%p A281687 N:= 1000: V:= Vector(2*N):
%p A281687 V[1]:= 1:
%p A281687 for n from 2 to 2*N by 2 do
%p A281687   if nops(numtheory:-invphi(n))>1 then V[n]:= 1 fi
%p A281687 od:
%p A281687 C:= map(round,SignalProcessing:-Convolution(V,V)):
%p A281687 seq((C[2*i-1]+V[i])/2,i=1..N); # _Robert Israel_, Jan 27 2017
%o A281687 (PARI) a(n) = sum(k=1, n, istotient(k) && istotient(2*n-k));
%Y A281687 Cf. A000010, A002202, A045917, A280867.
%K A281687 nonn,look
%O A281687 1,4
%A A281687 _Altug Alkan_, Jan 27 2017