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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-Fran├žois 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 July 6 00:43 EDT 2020. Contains 335475 sequences. (Running on oeis4.)