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 A291784 a(n) = (psi(n) + phi(n))/2. 15
 1, 2, 3, 4, 5, 7, 7, 8, 9, 11, 11, 14, 13, 15, 16, 16, 17, 21, 19, 22, 22, 23, 23, 28, 25, 27, 27, 30, 29, 40, 31, 32, 34, 35, 36, 42, 37, 39, 40, 44, 41, 54, 43, 46, 48, 47, 47, 56, 49, 55, 52, 54, 53, 63, 56, 60, 58 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is (A001615 + A000010)/2. It is easy to see that this is always an integer. If n is a power of a prime (including 1 and primes), then a(n) = n, and in any other case a(n) > n. - M. F. Hasler, Sep 09 2017 If n is in A006881, then a(n)=n+1. - Robert Israel, Feb 10 2019 REFERENCES Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004. See Section B41, p. 147. LINKS Hugo Pfoertner, Table of n, a(n) for n = 1..10000 N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence) MAPLE f:= proc(n) local P, p;   P:= numtheory:-factorset(n);   n*(mul((p-1)/p, p=P) + mul((p+1)/p, p=P))/2 end proc: map(f, [\$1..100]); # Robert Israel, Feb 10 2019 MATHEMATICA psi[n_] := If[n == 1, 1, n*Times @@ (1 + 1/FactorInteger[n][[All, 1]])]; a[n_] := (psi[n] + EulerPhi[n])/2; Array[a, 100] (* Jean-François Alcover, Feb 25 2019 *) PROG (PARI) A291784(n)=(eulerphi(n)+n*sumdivmult(n, d, issquarefree(d)/d))\2 \\ M. F. Hasler, Sep 03 2017 CROSSREFS Cf. A000010, A001615, A291785, A291786, A291787, A291788. Sequence in context: A114707 A000015 A306369 * A291934 A291785 A122411 Adjacent sequences:  A291781 A291782 A291783 * A291785 A291786 A291787 KEYWORD nonn AUTHOR N. J. A. Sloane, Sep 02 2017 STATUS approved

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Last modified April 10 17:00 EDT 2021. Contains 342852 sequences. (Running on oeis4.)