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

1,1

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

Formula

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

Prog

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

Crossrefs

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

Sequence in context: A328123 A110553 A330360 * A118893 A055792 A322243

Adjacent sequences: A078323 A078324 A078325 * A078327 A078328 A078329

Keyword

nonn

Author

Reinhard Zumkeller, Nov 23 2002

Extensions

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

Status

approved