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%I #14 Mar 03 2023 07:18:49
%S 3,4,1,7,9,2,5,4,13,15,8,9,19,8,13,4,3,16,25,27,4,16,9,18,13,32,1,35,
%T 19,18,31,8,32,9,43,16,12,17,47,49,23,27,1,53,55,16,41,23,36,61,7,4,
%U 28,24,65,36,27,4,69,71,27,8,21,17,3,72,77,47,32,81,47,36,36,49,87,8
%N Differences of consecutive powerful numbers (definition 1).
%C The term 1 appears infinitely often. Erdos conjectured that two consecutive 1's do not occur. (see Guy).
%D R. K. Guy, Unsolved Problems in Number Theory, B16
%H Reinhard Zumkeller, <a href="/A076446/b076446.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PowerfulNumber.html">Powerful numbers</a>
%F a(n) = A001694(n+1) - A001694(n).
%e The first two powerful numbers are 1 and 4, there difference is 3, so a(1)=3.
%t Differences[Join[{1},Select[Range[2000],Min[FactorInteger[#][[All, 2]]]>1&]]] (* _Harvey P. Dale_, Aug 27 2017 *)
%o (Haskell)
%o a076446 n = a076446_list !! (n-1)
%o a076446_list = zipWith (-) (tail a001694_list) a001694_list
%o -- _Reinhard Zumkeller_, Nov 30 2012
%Y Cf. A001694, A076444.
%K nonn
%O 1,1
%A _Jud McCranie_, Oct 15 2002
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