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

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, 10, 11, 10, 12, 11, 13, 10, 11, 12, 13, 12, 15, 13, 12, 13, 13, 12, 15, 14, 14, 14, 16, 15, 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

Offset: 1

Author

Altug Alkan, Jan 27 2017

Keywords

• nonn
• look

Comments

See also graph of A045917 ("Goldbach's comet"). - Altug Alkan, Jan 30 2017

Examples

			a(6) = 3 because 2 * 6 = 12 = 2 + 10 = 4 + 8 = 6 + 6 and 2, 4, 6, 8, 10 are in A002202.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Altug Alkan, Illustration Of Residue Classes Modulo 6

Crossrefs

Cf. A000010, A002202, A045917, A280867.

Programs

Maple

N:= 1000: V:= Vector(2*N):
V[1]:= 1:
for n from 2 to 2*N by 2 do
  if nops(numtheory:-invphi(n))>1 then V[n]:= 1 fi
od:
C:= map(round,SignalProcessing:-Convolution(V,V)):
seq((C[2*i-1]+V[i])/2,i=1..N); # Robert Israel, Jan 27 2017

PARI

a(n) = sum(k=1, n, istotient(k) && istotient(2*n-k));