%I #9 Nov 10 2024 21:47:53

%S 2,3,5,6,7,10,11,13,14,17,18,19,22,23,26,29,30,31,34,37,38,41,43,46,

%T 47,53,58,59,61,62,66,67,70,71,73,74,79,82,83,86,89,90,94,97,98,101,

%U 102,103,106,107,109,113,118,122,127,130,131,134,137,138,139,142

%N Numbers with only one factorization into factors > 1 with integer mean (namely, as a singleton).

%H Antti Karttunen, <a href="/A327906/b327906.txt">Table of n, a(n) for n = 1..10000</a>

%e There are 4 factorizations of 24 with integer mean, namely:

%e (24)

%e (4*6)

%e (2*12)

%e (2*3*4)

%e so 24 is not in the sequence.

%t facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];

%t Select[Range[100],Length[Select[facs[#],IntegerQ[Mean[#]]&]]==1&]

%o (PARI)

%o A326622(n, m=n, facsum=0, facnum=0) = if(1==n,facnum > 0 && 1==denominator(facsum/facnum), my(s=0); fordiv(n, d, if((d>1)&&(d<=m), s += A326622(n/d, d, facsum+d, facnum+1))); (s)); \\ _Antti Karttunen_, Nov 10 2024

%o isA327906(n) = (1==A326622(n)); \\ _Antti Karttunen_, Nov 10 2024

%Y Complement of A327907.

%Y Positions of 1's in A326622.

%Y Cf. A001055, A051293, A067538, A078175, A123528/A123529, A316413, A326515, A326516, A326666, A326667, A326671.

%K nonn

%O 1,1

%A _Gus Wiseman_, Sep 30 2019