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