A078326 - OEIS

%I #26 Feb 16 2025 08:32:48

%S 9,289,676,9801,12168,235225,332929,465125,1825201,11309769,384199201,

%T 592192225,4931691076,5425069448,13051463049,221322261601,

%U 443365544449,865363202001,8192480787001,11968683934832,13325427460801,15061377048201,28821995554248

%N Numbers n such that n-1 and n are a pair of consecutive powerful numbers.

%C a(n) = u*rad(u) = v*rad(v)+1 for appropriate u, v, where rad(n) = A007947(n) is the squarefree kernel.

%C Also numbers n such that n(n-1) is a powerful number. - _Charles R Greathouse IV_, Aug 08 2013

%H Donovan Johnson, <a href="/A078326/b078326.txt">Table of n, a(n) for n = 1..39</a> (terms < 10^22)

%H Jérôme Germoni, <a href="http://images-archive.math.cnrs.fr/Nombres-puissants-au-bac-S.html">Nombres puissants au bac S</a>, Images des Mathématiques, CNRS, 2021 (in French).

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PowerfulNumber.html">Powerful Number</a>

%F a(n) = A060355(n)+1.

%o (PARI) is(n)=ispowerful(n-1)&&ispowerful(n) \\ _Charles R Greathouse IV_, Aug 08 2013

%Y Cf. A078310, A064549, A078315, A078325, A060355, A078326.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Nov 23 2002

%E a(22)-a(23) from _Donovan Johnson_, Jul 29 2011