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.

A319057 Minimum sum of a strict factorization of n into factors > 1.

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%I A319057 #17 Oct 22 2018 02:41:01
%S A319057 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,
%T A319057 29,10,31,12,14,19,12,11,37,21,16,11,41,12,43,15,14,25,47,12,49,15,20,
%U A319057 17,53,14,16,13,22,31,59,12,61,33,16,14,18,16,67,21,26
%N A319057 Minimum sum of a strict factorization of n into factors > 1.
%C A319057 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
%H A319057 Charlie Neder, <a href="/A319057/b319057.txt">Table of n, a(n) for n = 1..1000</a>
%e A319057 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.
%t A319057 strfacs[n_]:=If[n<=1,{{}},Join@@Table[(Prepend[#,d]&)/@Select[strfacs[n/d],Min@@#>d&],{d,Rest[Divisors[n]]}]];
%t A319057 Table[Min[Total/@strfacs[n]],{n,100}]
%Y A319057 Cf. A001055, A007716, A045778, A056239, A162247, A215366, A246868, A318871, A318953, A318954.
%K A319057 nonn
%O A319057 1,2
%A A319057 _Gus Wiseman_, Sep 09 2018