|
| |
|
|
A123174
|
|
a(n) is the least triprime T for which the Mertens function M(T) = n.
|
|
1
|
|
|
|
20, 8, 27, 164, 98, 345, 343, 222, 555, 590, 1358, 1388, 1394, 1407, 1406, 1419, 3435, 3231, 3237, 3236, 3245, 3243, 3275, 3282, 3292, 3297, 8163, 8361, 8666, 8662, 8494, 8493, 8538, 8590
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
-3,1
|
|
|
LINKS
|
|
|
|
FORMULA
|
|
|
|
EXAMPLE
|
a(-3) = 20 = 2^2 * 5 = the first triprime T for which the Mertens function M(T) = -3.
a(-2) = 8 = 2^3 = the first triprime T for which the Mertens function M(T) = -2.
a(-1) = 27 = 3^3 = the first triprime T for which the Mertens function M(T) = -1.
a(0) = 164 = 2^2 * 41 = min{A014612 INTERSECTION A028442} = the first triprime T for which the Mertens function M(T) = 0.
a(1) = 98 = 2 * 7^2 = min{A014612 INTERSECTION A118684} = the first triprime T for which the Mertens function M(T) = 1.
a(2) = 335 = 3 * 5 * 23 = the first triprime T for which the Mertens function M(T) = 2.
a(3) = 343 = 7^3 = the first triprime T for which the Mertens function M(T) = 3.
|
|
|
MAPLE
|
isA014612 := proc(n) option remember ; RETURN( numtheory[bigomega](n) = 3) ; end: A008683 := proc(n) option remember ; numtheory[mobius](n) ; end: A002321 := proc(n) option remember ; add(A008683(k), k=1..n) ; end: A123174 := proc(n) local T; for T from 2 do if isA014612(T) then if A002321(T) = n then RETURN(T) ; fi; fi; od: end: for n from -3 to 30 do printf("%d, ", A123174(n)) ; od: # R. J. Mathar, Jan 27 2009
|
|
|
MATHEMATICA
|
M[k_] := M[k] = MoebiusMu[Range[k]] // Total;
PO[k_] := PO[k] = PrimeOmega[k];
a[n_] := a[n] = Module[{k}, For[k = 8, True, k++, If[PO[k] == 3 && M[k] == n, Return[k]]]];
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
a(2)=335 replaced with 345 and sequence extended to a(30) by R. J. Mathar, Jan 27 2009
|
|
|
STATUS
|
approved
|
| |
|
|
