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A073542
Numbers k such that 1/(1/phi(k) + 1/phi(k+1)) is an integer.
6
3, 12, 13, 15, 35, 36, 37, 55, 61, 72, 73, 86, 90, 96, 99, 104, 108, 119, 126, 154, 157, 164, 175, 182, 192, 193, 194, 244, 255, 277, 286, 296, 304, 313, 352, 362, 364, 369, 378, 397, 421, 432, 455, 457, 483, 495, 515, 527, 541, 545, 560, 576, 584, 602, 609
OFFSET
1,1
FORMULA
Is a(n) asymptotic to c*n^(3/2) with 1<c<1.5? [This conjecture is false, see plots. - Vaclav Kotesovec, Feb 15 2019]
EXAMPLE
1/phi(286) + 1/phi(287) = 1/120 + 1/240 = 1/80 so 286 is in the sequence.
MATHEMATICA
Select[Range[700], IntegerQ[1/(1/EulerPhi[ # ]+1/EulerPhi[ #+1])]&]
PROG
(PARI) isok(k) = numerator(1/eulerphi(k) + 1/eulerphi(k+1)) == 1; \\ Michel Marcus, Feb 18 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Aug 27 2002
EXTENSIONS
Edited by Dean Hickerson, Aug 31 2002
STATUS
approved