A307853 Number of solutions to phi(a) + phi(b) = n, where phi is Euler's totient function A000010.

0, 4, 12, 9, 16, 24, 16, 40, 20, 62, 8, 68, 24, 92, 0, 89, 24, 104, 16, 136, 20, 134, 8, 180, 40, 180, 0, 234, 8, 180, 8, 232, 28, 186, 0, 288, 32, 196, 0, 327, 36, 270, 16, 388, 12, 234, 8, 474, 44, 266, 0, 472, 8, 312, 8, 514, 12, 278, 8, 554, 36, 274, 0, 605, 32

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{j=1..n-1} A014197(j)*A014197(n-j) for n > 1. - Jinyuan Wang, May 03 2019

Example

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

Prog

(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))))};
a(n) = sum(x=1, n-1, f(x)*f(n-x)); \\ Jinyuan Wang, May 03 2019

Crossrefs

Cf. A000010, A014197.

A307854 gives the positions of zeros.

Sequence in context: A231100 A229179 A273172 * A334768 A247327 A348419

Adjacent sequences: A307850 A307851 A307852 * A307854 A307855 A307856

Keyword

nonn

Author

Jack Zhang, May 01 2019

Extensions

More terms from Jinyuan Wang, May 03 2019

Status

approved