A307853 - OEIS

%I #22 Jul 19 2019 17:11:44

%S 0,4,12,9,16,24,16,40,20,62,8,68,24,92,0,89,24,104,16,136,20,134,8,

%T 180,40,180,0,234,8,180,8,232,28,186,0,288,32,196,0,327,36,270,16,388,

%U 12,234,8,474,44,266,0,472,8,312,8,514,12,278,8,554,36,274,0,605,32

%N Number of solutions to phi(a) + phi(b) = n, where phi is Euler's totient function A000010.

%H Amiram Eldar, <a href="/A307853/b307853.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = Sum_{j=1..n-1} A014197(j)*A014197(n-j) for n > 1. - _Jinyuan Wang_, May 03 2019

%e a(2) = 4: the pairs (a,b) are (1,1), (1,2), (2,1), (2,2)

%e a(3) = 12: the pairs (a,b) are (1,3), (1,4), (1,6), (2,3), (2,4), (2,6), (3,1), (3,2), (4,1), (4,2), (6,1), (6,2)

%o (PARI) f(n, m=1) = { n==1 && return(1+(m<2)); my(p, q); sumdiv(n, d, if( d>=m && isprime(d+1), sum( i=0, valuation(q=n\d, p=d+1), f(q\p^i, p))))};

%o a(n) = sum(x=1,n-1,f(x)*f(n-x)); \\ _Jinyuan Wang_, May 03 2019

%Y Cf. A000010, A014197.

%Y A307854 gives the positions of zeros.

%K nonn

%O 1,2

%A _Jack Zhang_, May 01 2019

%E More terms from _Jinyuan Wang_, May 03 2019