A076444 - OEIS

%I #19 Feb 16 2025 08:32:47

%S 8,25,1,4,4,214369,1,1,16,2187,16,4,36,30459361,1,9,8,9,8,16,4,27,4,1,

%T 100,1,9,4,196,6859,1,4,16,899236854927,1,36,27,1331,25,9,8,

%U 518436000625,200,64,4,243,25,1,32,625,49,144,72,27,9,8,64,109503,49,4,64,3025,1,8,16

%N Smallest powerful number (definition 1) such that a(n)+n is also powerful.

%C McDaniel proved that a(n) exists for all n > 0.

%C Sister sequence of a(n)+n given by A103952.

%C a(110) > 10^22. - Donovan Johnson, Nov 19 2011

%D R. K. Guy, Unsolved Problems in Number Theory, B16

%H Donovan Johnson, <a href="/A076444/b076444.txt">Table of n, a(n) for n = 1..109</a>

%H Wayne L. McDaniel, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/20-1/mcdaniel.pdf">Representations of every integer as the difference of powerful numbers</a>, Fibonacci Quarterly 20 (1982), pp. 85-87.

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

%e 214369=463^2 and 214375=5^4*7^3 are the smallest pair of powerful numbers differing by 6, so a(6)=214369.

%Y Cf. A001694, A103952, A103953, A103954.

%K nonn,changed

%O 1,1

%A _Jud McCranie_, Oct 13 2002

%E More terms from _Max Alekseyev_, Feb 22 2005