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

1,4

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Altug Alkan, Illustration Of Residue Classes Modulo 6

Example

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

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

Prog

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

Crossrefs

Cf. A000010, A002202, A045917, A280867.

Sequence in context: A330561 A048688 A092695 * A033270 A285507 A103264

Adjacent sequences: A281684 A281685 A281686 * A281688 A281689 A281690

Keyword

nonn,look

Author

Altug Alkan, Jan 27 2017

Status

approved