A078326 Numbers n such that n-1 and n are a pair of consecutive powerful numbers.

9, 289, 676, 9801, 12168, 235225, 332929, 465125, 1825201, 11309769, 384199201, 592192225, 4931691076, 5425069448, 13051463049, 221322261601, 443365544449, 865363202001, 8192480787001, 11968683934832, 13325427460801, 15061377048201, 28821995554248

Offset: 1

Author

Reinhard Zumkeller, Nov 23 2002

Keywords

• nonn

Comments

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

Also numbers n such that n(n-1) is a powerful number. - Charles R Greathouse IV, Aug 08 2013

Links

• Donovan Johnson, Table of n, a(n) for n = 1..39 (terms < 10^22)
• Jérôme Germoni, Nombres puissants au bac S, Images des Mathématiques, CNRS, 2021 (in French).
• Eric Weisstein's World of Mathematics, Powerful Number

Crossrefs

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

Programs

PARI

is(n)=ispowerful(n-1)&&ispowerful(n) \\ Charles R Greathouse IV, Aug 08 2013

Formula

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

Extensions

a(22)-a(23) from Donovan Johnson, Jul 29 2011