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A229978
Numbers such that (2n+1) + phi(2n+1) <= sigma(2n+1)
1
7, 22, 31, 37, 52, 67, 82, 94, 97, 112, 115, 127, 136, 142, 148, 157, 172, 178, 187, 199, 202, 214, 217, 220, 232, 241, 247, 262, 277, 283, 292, 304, 307, 322, 325, 337, 346, 352, 367, 382, 388, 397, 409, 412, 427, 430, 442, 445, 451, 457, 472, 487, 502, 517, 532, 535, 547, 562, 577, 592, 598, 607, 622, 637, 643, 652, 661, 667, 682, 697, 712, 724, 727, 742, 757, 772, 787, 802, 808, 817
OFFSET
1,1
COMMENTS
It appears that the equation x + phi(x) = sigma(x) has the unique solution x=2. It is easy to show that this is the only even solution to the equation, but for odd solutions this is less obvious. The present sequence is motivated by the observation that for most odd numbers, the l.h.s. is larger than the r.h.s. (while the opposite is the case for all even numbers). (See also formulas in A228947.)
PROG
(PARI) select(n->(2*n+1+eulerphi(2*n+1)<sigma(2*n+1)), vector(900, n, n-1))
CROSSREFS
Cf. A228947, A051612 and references there, A000203, A000010.
Sequence in context: A041090 A042639 A287166 * A316840 A063240 A063157
KEYWORD
nonn
AUTHOR
M. F. Hasler, Oct 05 2013
STATUS
approved