A217784 Triprimes to triprime powers.

16777216, 429981696, 11019960576, 25600000000, 68719476736, 282429536481, 377801998336, 656100000000, 8916100448256, 9682651996416, 14048223625216, 16815125390625, 39062500000000, 53459728531456, 248155780267521, 360040606269696, 457163239653376, 576480100000000

Offset

1,1

Comments

Triprimes are numbers with exactly three prime factors: A014612.

This is to triprimes as primes are to A053810 (Prime powers of prime numbers) and as semiprimes are to A113877 (Semiprimes to semiprime powers). - Jonathan Vos Post, Mar 26 2013

a(n) increases roughly as n^8, because 9669 of the first 10000 terms are powers of 8. - Kevin L. Schwartz and Christian N. K. Anderson, Jun 05 2013

Links

Kevin L. Schwartz and Christian N. K. Anderson, Table of n, a(n) for n = 1..1000

Example

429981696 = 8^12.
a(10) = 9682651996416 = 42^8 = (2*3*7)^(2*2*2).

Prog

(R) library(gmp); istriprime=function(x) ifelse(as.bigz(x)<8, F, length(factorize(x))==3)as.bigz(which(sapply(1:200, istriprime)))->trp; maxy=tail(trp, 1)^trp[1]; len=0; y=as.bigz(rep(0, 100))
for(i in 1:length(trp)) { j=0; while((n=trp[i]^trp[(j=j+1)])<=maxy) y[(len=len+1)]=n }
y[1:len]->y; y[order(as.numeric(y))]
-- Kevin L. Schwartz and Christian N. K. Anderson, Jun 05 2013

Crossrefs

Cf. A014612, A053810, A113877, A129539.

Sequence in context: A057070 A067494 A177081 * A017000 A017072 A017264

Adjacent sequences: A217781 A217782 A217783 * A217785 A217786 A217787

Keyword

nonn

Author

Kevin L. Schwartz and Christian N. K. Anderson, Mar 24 2013

Status

approved