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 A256241 Numbers n whose Euler's totient function phi(n), divided by two, plus one, p = (phi(n) / 2) + 1, is a divisor of n. 1
 4, 6, 12, 15, 20, 21, 28, 30, 33, 39, 42, 44, 51, 52, 57, 66, 68, 69, 76, 78, 87, 92, 93, 102, 111, 114, 116, 123, 124, 129, 138, 141, 148, 159, 164, 172, 174, 177, 183, 186, 188, 201, 212, 213, 219, 222, 236, 237, 244, 246, 249, 258, 267, 268, 282, 284, 291, 292, 303, 309, 316, 318, 321, 327, 332, 339, 354, 356, 366 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS p is always a prime factor of n as well. Except for the case n=6, p is always the greatest prime factor of n. (n/p) is an upper bound on the rest of the prime factors 'q' of n, so always q <= (n/p). LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 David Morales Marciel, Euler's Totient function statement proposal EXAMPLE For n = 4, phi(n) = 2, p = (phi(n)/2)+1 = 2, is prime and is a prime factor of 4. For n = 6, phi(n) = 2, p = (phi(n)/2)+1 = 2, is prime and is a prime factor of 6. MATHEMATICA aQ[n_] := Divisible[n, 1 + EulerPhi[n] / 2]; Select[Range, aQ] (* Amiram Eldar, Nov 06 2019 *) PROG (Python) from sympy import totient [n for n in range(1, 10**5) if n%((totient(n)/2)+1)==0] (PARI) isok(n) = (n % (eulerphi(n)/2+1)) == 0; \\ Michel Marcus, Apr 20 2015 (MAGMA) [k:k in [1..370]| IsIntegral(k/(EulerPhi(k)/2+1))]; // Marius A. Burtea, Nov 06 2019 CROSSREFS Cf. A000010. Sequence in context: A131863 A074870 A251630 * A247632 A104236 A265225 Adjacent sequences:  A256238 A256239 A256240 * A256242 A256243 A256244 KEYWORD nonn AUTHOR David Morales Marciel, Apr 19 2015 EXTENSIONS Removed long Python code, and added very simple Python program (two lines) with sympy as suggested by the Editor. STATUS approved

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Last modified July 2 02:22 EDT 2020. Contains 335389 sequences. (Running on oeis4.)