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A073460
a(n) = smallest solution x to n + pi(x) = phi(x), or 0 if no such solution exists.
0
30, 6, 2, 1, 7, 26, 21, 11, 13, 180, 46, 17, 19, 25, 39, 23, 64, 74, 174, 51, 29, 31, 57, 104, 94, 228, 37, 69, 116, 41, 43, 258, 65, 47, 81, 87, 134, 99, 53, 280, 146, 77, 135, 59, 61, 111, 166, 172, 184, 67, 91, 408, 71, 73, 194, 129, 202, 780, 79, 212, 115, 83
OFFSET
-2,1
COMMENTS
Although pi takes all values, solutions are not guaranteed since nontotient numbers exist.
First possible holes (k>10^6) are for n = -3, 63, 73, 144, 162, 185, 204, 228, 233, 256, 264,...
FORMULA
a(n)=Min{x; A000010(x)-A000720(x)=n}
EXAMPLE
n=13: Phi[13]=12, Pi[13]=6, a[12-6]=a(6)=13; n=63: no solution was found at x<=1000000.
MATHEMATICA
Do[k = 1; While[ EulerPhi[k] != PrimePi[k] + n, k++ ]; Print[k], {n, -2, 62}]
KEYWORD
nonn
AUTHOR
Labos Elemer, Aug 02 2002
EXTENSIONS
Edited by Robert G. Wilson v, Aug 12 2002
STATUS
approved