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Moebius function in the ranked poset of factorizations of n into factors > 1, evaluated at the minimum (the prime factorization of n).
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%I #10 Feb 18 2024 12:27:34

%S 0,1,1,-1,1,-1,1,0,-1,-1,1,1,1,-1,-1,0,1,1,1,1,-1,-1,1,-1,-1,-1,0,1,1,

%T 2,1,0,-1,-1,-1,-1,1,-1,-1,-1,1,2,1,1,1,-1,1,1,-1,1,-1,1,1,-1,-1,-1,

%U -1,-1,1,-3,1,-1,1,0,-1,2,1,1,-1,2,1,2,1,-1,1,1

%N Moebius function in the ranked poset of factorizations of n into factors > 1, evaluated at the minimum (the prime factorization of n).

%C If x and y are factorizations of the same integer and it is possible to produce x by further factoring the factors of y, flattening, and sorting, then x <= y.

%F Product_{k>=2} 1/(1-a(n)/n^s) = 1+P(s), Re(s)>1, where P(s) is the prime zeta function. - _Tian Vlasic_, Jan 25 2024

%e The factorizations of 60 followed by their Moebius values are the following. The second column sums to 0, as required.

%e (2*2*3*5) -> -3

%e (2*2*15) -> 1

%e (2*3*10) -> 2

%e (2*5*6) -> 2

%e (2*30) -> -1

%e (3*4*5) -> 2

%e (3*20) -> -1

%e (4*15) -> -1

%e (5*12) -> -1

%e (6*10) -> -1

%e (60) -> 1

%Y Cf. A000837, A001055, A007716, A045778, A162247, A275024, A281113, A299202, A317144, A317145.

%K sign

%O 1,30

%A _Gus Wiseman_, Jul 22 2018