A327906 - OEIS

A327906

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

2, 3, 5, 6, 7, 10, 11, 13, 14, 17, 18, 19, 22, 23, 26, 29, 30, 31, 34, 37, 38, 41, 43, 46, 47, 53, 58, 59, 61, 62, 66, 67, 70, 71, 73, 74, 79, 82, 83, 86, 89, 90, 94, 97, 98, 101, 102, 103, 106, 107, 109, 113, 118, 122, 127, 130, 131, 134, 137, 138, 139, 142

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OFFSET

1,1

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

EXAMPLE

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

(24)

(4*6)

(2*12)

(2*3*4)

so 24 is not in the sequence.

MATHEMATICA

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

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

PROG

(PARI)

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

isA327906(n) = (1==A326622(n)); \\ Antti Karttunen, Nov 10 2024

CROSSREFS

Complement of A327907.

Positions of 1's in A326622.

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

Sequence in context: A359782 A235991 A377871 * A333866 A325362 A339563

Adjacent sequences: A327903 A327904 A327905 * A327907 A327908 A327909

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 30 2019

STATUS

approved