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.
%I A378700 #7 Dec 06 2024 11:10:14 %S A378700 5,11,10,1,10,19,1,4,2,22,12,27,1,11,2,14,6,28,26,9,0,41,3,26,13,25,0, %T A378700 10,35,11,10,0,26,26,8,10,5,26,30,17,11,52,13,12,56,1,20,9,34,69,1,69, %U A378700 37,3,38,0,14,57,11,39,23,15,26,18,6,36,3,30,27,27,97 %N A378700 Number of k in A126706 between powerful numbers that are not prime powers. %C A378700 Within the sequence S = A126706 of powerful numbers, we have numbers k that are powerful (in A286708) and numbers m that are not powerful (in A332785). This sequence is the number of k between m. %H A378700 Michael De Vlieger, <a href="/A378700/b378700.txt">Table of n, a(n) for n = 1..10000</a> %H A378700 Michael De Vlieger, <a href="/A378700/a378700.png">Log log scatterplot of a(n)</a>, n = 1..11210, rendering a(n) = 0 instead as 1/2 for visibility. %e A378700 We partition S = A126706 by numbers k in A286708 (in brackets) and derive the following irregular table: %e A378700 12, 18, 20, 24, 28, [36]; hence a(1) = 5, %e A378700 40, 44, 45, 48, 50, 52, 54, 56, 60, 63, 68, [72]; a(2) = 11, %e A378700 75, 76, 80, 84, 88, 90, 92, 96, 98, 99, [100]; a(3) = 10, %e A378700 104, [108]; a(4) = 1, %e A378700 112, 116, 117, 120, 124, 126, 132, 135, 136, 140, [144]; a(5) = 10, etc. %t A378700 s = Select[Range[2^16], Nor[SquareFreeQ[#], PrimePowerQ[#]] &]; -1 + Length /@ TakeList[s, Prepend[Differences[#], First[#]] &@ Position[s, _Integer?(Divisible[#, Apply[Times, FactorInteger[#][[All, 1]] ]^2] &)][[All, 1]] ] %Y A378700 Cf. A001694, A126706, A286708, A332785. %K A378700 nonn,easy %O A378700 1,1 %A A378700 _Michael De Vlieger_, Dec 04 2024