A067266 Numbers n such that omega(n)=M(n) where omega(n) is A001221(n) and M(n) is the Mertens function A002321(n).

95, 96, 97, 217, 228, 335, 337, 339, 342, 349, 395, 397, 398, 417, 543, 544, 546, 550, 603, 604, 605, 802, 804, 807, 808, 809, 817, 819, 820, 871, 872, 873, 879, 881, 901, 922, 930, 938, 945, 947, 949, 952, 962, 969, 971, 973, 975, 979, 981, 989, 991, 993

Offset: 1

Author

Benoit Cloitre, Feb 21 2002

Keywords

• easy
• nonn

Comments

"omega(n)" (in the definition) means the number of prime factors of n counted without multiplicity, A001221. - Harvey P. Dale, Jul 14 2014

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1369 terms from Robert Israel)

Crossrefs

Cf. A001221, A002321.

Programs

Haskell

a067266 n = a067266_list !! (n-1)
a067266_list = filter (\x -> a001221 x == a002321 x) [1..]
-- Reinhard Zumkeller, Jul 14 2014

Maple

N:= 10^4: # to get all terms up to N
A:= [seq(numtheory[mobius](n),n=1..N)]:
Mertens:= map(round,Statistics:-CumulativeSum(A)):
omega:= t -> nops(numtheory:-factorset(t)):
select(t -> omega(t) = Mertens[t], [$1..N]); # Robert Israel, Jul 14 2014

Mathematica

With[{nn=1000},Flatten[Position[Thread[{Accumulate[Array[ MoebiusMu,nn]], PrimeNu[ Range[ nn]]}],?(First[#]==Last[#]&),{1},Heads->False]]] (* _Harvey P. Dale, Jul 14 2014 *)

PARI

isok(n) = (omega(n) == mertens(n)); \\ Michel Marcus, Sep 24 2013