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A067266 Numbers n such that omega(n)=M(n) where omega(n) is A001221(n) and M(n) is the Mertens function A002321(n). 1
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 (list; graph; refs; listen; history; text; internal format)
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

Robert Israel and 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

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Last modified January 26 22:05 EST 2022. Contains 350601 sequences. (Running on oeis4.)