A085252 Number of ways to write n as sum of two powerful numbers (A001694).

0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 2, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 2, 1, 1, 2, 1, 0, 0, 2, 2, 0, 1, 1, 1, 0, 0, 1, 0, 2, 0, 2, 1, 1, 0, 0, 2, 1, 1, 0, 1, 0, 1, 1, 2, 0, 0, 2, 0, 0, 0, 2, 2, 1, 0, 2, 0, 0, 0, 2, 2, 1, 0, 0, 2, 0, 0, 1, 2, 1, 1, 0, 0, 0, 0, 1, 2, 1, 1, 1, 1, 0

Offset

1,17

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Powerful Number.

Formula

a(A085253(n)) = 0.

a(A076871(n)) > 0.

a(A085254(n)) = 1.

a(A085255(n)) > 1.

Example

a(81) = 2: 81 = 9 + 72 = A001694(4) + A001694(12) = 32 + 49 = A001694(8) + A001694(10).

Mathematica

With[{m = 120}, pow = Select[Range[m], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &]; BinCounts[Select[Plus @@@ Union[Sort /@ Tuples[pow, {2}]], # <= m &], {1, m, 1}]] (* Amiram Eldar, Jan 30 2023 *)

Crossrefs

Cf. A001694, A076871, A085253, A085254, A085255.

Sequence in context: A060838 A206567 A362422 * A250214 A073423 A219180

Adjacent sequences: A085249 A085250 A085251 * A085253 A085254 A085255

Keyword

nonn

Author

Reinhard Zumkeller, Jun 23 2003

Status

approved