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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, Powerful Number.
Eric Weisstein's World of Mathematics, Squarefree.
FORMULA
a(n) > 0 for n > 1 (proof?).
a(A085258(n)) = n and a(i) <> n for i < A085258(n).
EXAMPLE
a(10) = 3: 10 = 1 + 9 = A005117(1) + A001694(4) = 2 + 8 = A005117(2) + A001694(3) = 6 + 4 = A005117(5) + A001694(2).
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
Sequence in context: A071444 A232441 A328701 * A352889 A230507 A352888
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jun 23 2003
STATUS
approved

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Last modified March 28 07:48 EDT 2024. Contains 371235 sequences. (Running on oeis4.)