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A307853
Number of solutions to phi(a) + phi(b) = n, where phi is Euler's totient function A000010.
2
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
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
A307854 gives the positions of zeros.
Sequence in context: A231100 A229179 A273172 * A334768 A247327 A348419
KEYWORD
nonn
AUTHOR
Jack Zhang, May 01 2019
EXTENSIONS
More terms from Jinyuan Wang, May 03 2019
STATUS
approved