cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A085255 Numbers having at least two representations as a sum of two powerful numbers (A001694).

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%I A085255 #13 Feb 16 2025 08:32:50
%S A085255 17,33,36,40,41,50,52,57,65,68,72,73,76,80,81,85,89,97,104,108,109,
%T A085255 113,116,117,125,129,130,132,133,136,137,144,145,148,152,153,157,160,
%U A085255 164,170,172,177,180,185,189,193,197,200,201,204,205,208,209,216,221
%N A085255 Numbers having at least two representations as a sum of two powerful numbers (A001694).
%H A085255 Amiram Eldar, <a href="/A085255/b085255.txt">Table of n, a(n) for n = 1..10000</a>
%H A085255 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PowerfulNumber.html">Powerful Number</a>.
%F A085255 A085252(a(n)) > 1.
%t A085255 With[{m = 222}, pow = Select[Range[m], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &]; Position[BinCounts[Select[Plus @@@ Union[Sort /@ Tuples[pow, {2}]], # <= m &], {1, m, 1}], _?(# > 1 &)] // Flatten] (* _Amiram Eldar_, Jan 30 2023 *)
%Y A085255 Cf. A001694, A076871, A085252, A085253, A085254.
%K A085255 nonn
%O A085255 1,1
%A A085255 _Reinhard Zumkeller_, Jun 23 2003