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

1,1

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)

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 *)

Prog

(PARI) isok(n) = (omega(n) == mertens(n)); \\ Michel Marcus, Sep 24 2013
(Haskell)
a067266 n = a067266_list !! (n-1)
a067266_list = filter (\x -> a001221 x == a002321 x) [1..]
-- Reinhard Zumkeller, Jul 14 2014

Crossrefs

Cf. A001221, A002321.

Sequence in context: A093007 A033415 A300007 * A171403 A055467 A057654

Adjacent sequences: A067263 A067264 A067265 * A067267 A067268 A067269

Keyword

easy,nonn

Author

Benoit Cloitre, Feb 21 2002

Status

approved