A306146 Numbers k such that A000010(A023900(k)) = A023900(A000010(k)).

1, 14, 22, 28, 44, 46, 56, 75, 88, 92, 94, 112, 118, 166, 176, 184, 188, 214, 224, 236, 332, 334, 352, 358, 368, 375, 376, 422, 428, 448, 454, 472, 526, 639, 662, 664, 668, 694, 704, 716, 718, 736, 752, 766, 844, 856, 867, 896, 908, 926, 934, 944, 958, 1006, 1052, 1075, 1094, 1126, 1142, 1174, 1179, 1324

Offset: 1

Author

Torlach Rush, Aug 11 2018

Keywords

• nonn

Comments

No term is a product of an odd number of distinct prime factors (because then A023900 is negative, i.e., contains no terms from A030230).

For known terms:

- a(n) is nonsquarefree iff A000010(n) is nonsquarefree.

- If a(n) is squarefree then A000010(n) and A023900(n) are both squarefree.

Examples

			75 is a term because A000010(A023900(75)) = A023900(A000010(75)) = 4.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A023900, A030230.

Programs

Maple

isA306146 := proc(n)
    local a239 ;
    a239 := A023900(n) ;
    if a239 >= 1 then
        simplify( numtheory[phi](a239) = A023900(numtheory[phi](n)) );
    else
        false;
    end if;
end proc:
for n from 1 to 1000 do
    if isA306146(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Feb 14 2019

Mathematica

f[p_, e_] := 1 - p; d[1] = 1; d[n_] := Times @@ (f @@@ FactorInteger[n]); Select[Range[1324],(d1 = d[#]) > 0 && d[EulerPhi[#]] == EulerPhi[d1] &] (* Amiram Eldar, Feb 19 2020 *)

PARI

a023900(n) = sumdivmult(n, d, d*moebius(d))
is(n) = sdm = a023900(n); if(sdm < 0, return(0), sdmphi = a023900(eulerphi(n)); eulerphi(sdm) == sdmphi) \\ David A. Corneth, Aug 17 2018