|
|
A085257
|
|
Number of ways to write n as sum of a powerful and a squarefree number.
|
|
2
|
|
|
0, 1, 1, 1, 1, 2, 2, 1, 2, 3, 4, 2, 1, 4, 4, 2, 2, 4, 4, 2, 3, 4, 5, 2, 2, 4, 5, 3, 3, 7, 5, 4, 4, 5, 6, 2, 6, 9, 8, 4, 4, 9, 6, 4, 4, 8, 8, 4, 5, 7, 8, 3, 4, 6, 8, 5, 4, 6, 7, 5, 4, 9, 7, 4, 6, 10, 8, 5, 7, 9, 9, 3, 7, 10, 10, 2, 6, 12, 8, 5, 4, 10, 11, 5, 6, 11, 12, 5, 6, 8, 9, 6, 8, 11, 11, 6
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,6
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Squarefree.
|
|
FORMULA
|
a(n) > 0 for n > 1 (proof?).
|
|
EXAMPLE
|
|
|
MATHEMATICA
|
With[{m = 100}, pow = Select[Range[m], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &]; sqf = Select[Range[m], SquareFreeQ]; BinCounts[Select[Plus @@@ Tuples[{pow, sqf}], # <= m &], {1, m, 1}]] (* Amiram Eldar, Feb 12 2023 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|