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

5, 9, 7, 15, 27, 21, 11, 35, 13, 33, 105, 39, 17, 65, 19, 51, 195, 57, 23, 95, 171, 69, 285, 115, 29, 161, 31, 87, 483, 93, 261, 155, 37, 217, 465, 111, 41, 185, 43, 123, 555, 129, 47, 215, 387, 141, 645, 235, 53, 329, 705, 159, 987, 265, 59, 371, 61, 177

Offset

5,1

Comments

All terms are odd.

It seems that all composite terms not divisible by 3 form a supersequence of A292081. - Ivan N. Ianakiev, Oct 30 2023

Links

Michel Marcus, Table of n, a(n) for n = 5..1000

Example

The terms together with their prime factors (which sum to n) begin:
    5 = 5
    9 = 3*3
    7 = 7
   15 = 3*5
   27 = 3*3*3
   21 = 3*7
   11 = 11
   35 = 5*7
   13 = 13
   33 = 3*11
  105 = 3*5*7

Mathematica

nn=1000;
w=Table[Total[Times@@@DeleteCases[If[n==1, {}, FactorInteger[n]], {2, _}]], {n, nn}];
spnm[y_]:=Max@@Select[Union[y], Function[i, Union[Select[y, #<=i&]]==Range[i]]];
Table[Position[w, k][[1, 1]], {k, 5, spnm[Join[{1, 2, 3, 4}, Take[w, nn]/.(0->1)]]}]

Prog

(PARI) f(n) = my(f=factor(n), j=if (n%2, 1, 2)); sum(i=j, #f~, f[i, 1]*f[i, 2]); \\ A366840
a(n) = my(k=1); while (f(k) != n, k++); k; \\ Michel Marcus, Nov 02 2023

Crossrefs

This is the odd case of A056240.

Positions of first appearances in A366840 (sum of odd prime factors).

The partition triangle for this statistic is A366851, even A116598.

A001414 adds up prime factors, triangle A331416.

A019507 lists numbers with (even factor sum) = (odd factor sum).

A027746 lists prime factors, length A001222.

A087436 counts odd prime factors, even A007814.

A366528 adds up odd prime indices, triangle A113685 (without zeros A365067).

Cf. A031368, A036349, A056239, A066208, A100005, A112798, A239261, A257991, A335657, A366839.

Sequence in context: A160050 A055566 A255247 * A153610 A357464 A249385

Adjacent sequences: A366838 A366839 A366840 * A366842 A366843 A366844

Keyword

nonn

Author

Gus Wiseman, Oct 27 2023

Status

approved