A319057 - OEIS

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A319057

Minimum sum of a strict factorization of n into factors > 1.

0, 2, 3, 4, 5, 5, 7, 6, 9, 7, 11, 7, 13, 9, 8, 10, 17, 9, 19, 9, 10, 13, 23, 9, 25, 15, 12, 11, 29, 10, 31, 12, 14, 19, 12, 11, 37, 21, 16, 11, 41, 12, 43, 15, 14, 25, 47, 12, 49, 15, 20, 17, 53, 14, 16, 13, 22, 31, 59, 12, 61, 33, 16, 14, 18, 16, 67, 21, 26

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OFFSET

1,2

COMMENTS

a(n) >= A001414(n), with equality iff n is squarefree or four times a squarefree number (i.e., A000188(n) <= 2). - Charlie Neder, Sep 10 2018

LINKS

Charlie Neder, Table of n, a(n) for n = 1..1000

EXAMPLE

The strict factorizations of 48 are (48), (2*24), (3*16), (4*12), (6*8), (2*3*8), (2*4*6), with sums 48, 26, 19, 16, 14, 13, 12 respectively, so a(48) = 12.

MATHEMATICA

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

Table[Min[Total/@strfacs[n]], {n, 100}]

CROSSREFS

Cf. A001055, A007716, A045778, A056239, A162247, A215366, A246868, A318871, A318953, A318954.

Sequence in context: A134875 A134889 A303702 * A181894 A265535 A094802

Adjacent sequences: A319054 A319055 A319056 * A319058 A319059 A319060

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 09 2018

STATUS

approved