cp's OEIS Frontend

A366841 Least positive integer whose odd prime factors sum to n, starting with n = 5.

%I A366841 #18 Nov 06 2023 07:17:05
%S A366841 5,9,7,15,27,21,11,35,13,33,105,39,17,65,19,51,195,57,23,95,171,69,
%T A366841 285,115,29,161,31,87,483,93,261,155,37,217,465,111,41,185,43,123,555,
%U A366841 129,47,215,387,141,645,235,53,329,705,159,987,265,59,371,61,177
%N A366841 Least positive integer whose odd prime factors sum to n, starting with n = 5.
%C A366841 All terms are odd.
%C A366841 It seems that all composite terms not divisible by 3 form a supersequence of A292081. - _Ivan N. Ianakiev_, Oct 30 2023
%H A366841 Michel Marcus, <a href="/A366841/b366841.txt">Table of n, a(n) for n = 5..1000</a>
%e A366841 The terms together with their prime factors (which sum to n) begin:
%e A366841     5 = 5
%e A366841     9 = 3*3
%e A366841     7 = 7
%e A366841    15 = 3*5
%e A366841    27 = 3*3*3
%e A366841    21 = 3*7
%e A366841    11 = 11
%e A366841    35 = 5*7
%e A366841    13 = 13
%e A366841    33 = 3*11
%e A366841   105 = 3*5*7
%t A366841 nn=1000;
%t A366841 w=Table[Total[Times@@@DeleteCases[If[n==1,{},FactorInteger[n]],{2,_}]],{n,nn}];
%t A366841 spnm[y_]:=Max@@Select[Union[y],Function[i,Union[Select[y,#<=i&]]==Range[i]]];
%t A366841 Table[Position[w,k][[1,1]],{k,5,spnm[Join[{1,2,3,4},Take[w,nn]/.(0->1)]]}]
%o A366841 (PARI) f(n) = my(f=factor(n), j=if (n%2, 1, 2)); sum(i=j, #f~, f[i,1]*f[i,2]); \\ A366840
%o A366841 a(n) = my(k=1); while (f(k) != n, k++); k; \\ _Michel Marcus_, Nov 02 2023
%Y A366841 This is the odd case of A056240.
%Y A366841 Positions of first appearances in A366840 (sum of odd prime factors).
%Y A366841 The partition triangle for this statistic is A366851, even A116598.
%Y A366841 A001414 adds up prime factors, triangle A331416.
%Y A366841 A019507 lists numbers with (even factor sum) = (odd factor sum).
%Y A366841 A027746 lists prime factors, length A001222.
%Y A366841 A087436 counts odd prime factors, even A007814.
%Y A366841 A366528 adds up odd prime indices, triangle A113685 (without zeros A365067).
%Y A366841 Cf. A031368, A036349, A056239, A066208, A100005, A112798, A239261, A257991, A335657, A366839.
%K A366841 nonn
%O A366841 5,1
%A A366841 _Gus Wiseman_, Oct 27 2023