

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
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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((p1)/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] (* JeanFrançois 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



