A071616 Smallest even number divisible by 2n which is nontotient, i.e., in A005277.

14, 68, 90, 152, 50, 516, 14, 304, 90, 340, 154, 4008, 26, 308, 90, 608, 34, 2412, 38, 680, 714, 308, 230, 10128, 50, 364, 594, 728, 174, 8340, 62, 1984, 594, 68, 350, 7848, 74, 76, 234, 6800, 246, 5124, 86, 968, 90, 644, 94, 20256, 98, 1100, 510, 728, 318

Offset

1,1

Comments

a(n) = 2n*A071615(n).

Links

Donovan Johnson, Table of n, a(n) for n = 1..10000

Example

n=4: 2n=8 and number of terms in invphi(8k) is 5, 6, 10, 7, 9, 11, 3, 8, 17, 10, 6, 17, 3, 6, 17, 9, 9, 21, 0, 12, ... for k=1,2,...,20,...; zero appears first at k=19, so a(4) = 8k = 152.

Mathematica

invphi[n_, plist_] := Module[{i, p, e, pe, val}, If[plist=={}, Return[If[n==1, {1}, {}]]]; val={}; p=Last[plist]; For[e=0; pe=1, e==0||Mod[n, (p-1)pe/p]==0, e++; pe*=p, val=Join[val, pe*invphi[If[e==0, n, n*p/pe/(p-1)], Drop[plist, -1]]]]; Sort[val]]; invphi[n_] := invphi[n, Select[1+Divisors[n], PrimeQ]]; a[n_] := For[m=1, True, m++, If[invphi[2n*m]=={}, Return[2n*m]]] (* invphi[n, plist] is list of x with phi(x)=n and all prime divisors of x in plist. *)

Crossrefs

Cf. A000010, A002202, A005277, A071615.

Sequence in context: A221703 A064096 A250141 * A008529 A075480 A236164

Adjacent sequences: A071613 A071614 A071615 * A071617 A071618 A071619

Keyword

nonn

Author

Labos Elemer, May 27 2002

Extensions

Edited and extended by Robert G. Wilson v, May 28 2002 and by Dean Hickerson, Jun 04 2002

Status

approved