cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A067266 #31 Oct 27 2023 22:03:25
%S A067266 95,96,97,217,228,335,337,339,342,349,395,397,398,417,543,544,546,550,
%T A067266 603,604,605,802,804,807,808,809,817,819,820,871,872,873,879,881,901,
%U A067266 922,930,938,945,947,949,952,962,969,971,973,975,979,981,989,991,993
%N A067266 Numbers n such that omega(n)=M(n) where omega(n) is A001221(n) and M(n) is the Mertens function A002321(n).
%C A067266 "omega(n)" (in the definition) means the number of prime factors of n counted without multiplicity, A001221. - _Harvey P. Dale_, Jul 14 2014
%H A067266 Alois P. Heinz, <a href="/A067266/b067266.txt">Table of n, a(n) for n = 1..10000</a> (first 1369 terms from Robert Israel)
%p A067266 N:= 10^4: # to get all terms up to N
%p A067266 A:= [seq(numtheory[mobius](n),n=1..N)]:
%p A067266 Mertens:= map(round,Statistics:-CumulativeSum(A)):
%p A067266 omega:= t -> nops(numtheory:-factorset(t)):
%p A067266 select(t -> omega(t) = Mertens[t], [$1..N]); # _Robert Israel_, Jul 14 2014
%t A067266 With[{nn=1000},Flatten[Position[Thread[{Accumulate[Array[ MoebiusMu,nn]], PrimeNu[ Range[ nn]]}],_?(First[#]==Last[#]&),{1},Heads->False]]] (* _Harvey P. Dale_, Jul 14 2014 *)
%o A067266 (PARI) isok(n) = (omega(n) == mertens(n)); \\ _Michel Marcus_, Sep 24 2013
%o A067266 (Haskell)
%o A067266 a067266 n = a067266_list !! (n-1)
%o A067266 a067266_list = filter (\x -> a001221 x == a002321 x) [1..]
%o A067266 -- _Reinhard Zumkeller_, Jul 14 2014
%Y A067266 Cf. A001221, A002321.
%K A067266 easy,nonn
%O A067266 1,1
%A A067266 _Benoit Cloitre_, Feb 21 2002