A171607 Expressible as A*B^A in a nontrivial way.

8, 18, 24, 32, 50, 64, 72, 81, 98, 128, 160, 162, 192, 200, 242, 288, 324, 338, 375, 384, 392, 450, 512, 578, 648, 722, 800, 882, 896, 968, 1024, 1029, 1058, 1152, 1215, 1250, 1352, 1458, 1536, 1568, 1682, 1800, 1922, 2048, 2178, 2187, 2312, 2450, 2500, 2592

Offset: 1

Author

Robert Munafo, Dec 12 2009

Keywords

• nonn

Examples

			8=2*2^2. 24=3*2^3. 375=3*5^3.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• R. Munafo, Generalized Cullen and Woodall Numbers

Crossrefs

Cf. A171606. Union of the "KN^K" sequences A001105, A117642, A141046, ... or of the "NK^N" sequences A036289, A036290, A018215, A036291, ... but omitting the trivial initial terms.

Programs

PARI

is(n)=if(n<8, return(0)); for(a=2,logint(n\2,2), if(n%a==0 && ispower(n/a,a), return(1))); 0 \\ Charles R Greathouse IV, Feb 19 2017

PARI

list(lim)=my(v=List()); if(lim<8,return([])); for(a=2,logint(lim\2,2), for(b=2,sqrtnint(lim\a,a), listput(v,a*b^a))); Set(v) \\ Charles R Greathouse IV, Feb 19 2017

Formula

a(n) = 2n^2 - O(n^(5/3)). - Charles R Greathouse IV, Feb 19 2017