A257404 Numbers of the form p * q^p where p and q are primes, in increasing order.

8, 18, 24, 50, 81, 98, 160, 242, 338, 375, 578, 722, 896, 1029, 1058, 1215, 1682, 1922, 2738, 3362, 3698, 3993, 4418, 5618, 6591, 6962, 7442, 8978, 10082, 10658, 12482, 13778, 14739, 15309, 15625, 15842, 18818

Offset: 1

Author

William Brian Repko, Apr 22 2015

Keywords

• nonn

Examples

			(2,2):8, (2,3):18, (3,2):24, (2,5):50, (3,3):81, (2,7):98.
		

Crossrefs

Cf. some subsequences: A079704, A104126.

Programs

JavaScript

primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97];
results = [];
max = 2 * Math.pow(primes[primes.length-1],2);
for (i = 0; i < primes.length; i++) {
    for (j = 0; j  < primes.length; j++) {
        p = primes[i];
        q = primes[j];
        n = p * Math.pow(q,p);
        if (n <= max) {
            // add it
            results.push(n);
        } else {
            // break out of this loop
            break;
        }
    }
}
// sort results and print them
results.sort(function(a, b){return a-b}).valueOf();

Mathematica

max=10^5; p=q=2; Sort[Reap[While[2*q^2 <= max, While[(n=p*q^p) <= max, Sow@n; p=NextPrime@p]; p=2; q=NextPrime@q ]][[2,1]]] (* Giovanni Resta, May 19 2015 *)

PARI

is(n)={bittest(6,#n=factor(n)~)||return;#n==1&&return(n[1,1]+1==n[2,1]);(n[2,1]==1&&n[2,2]==n[1,1])||(n[2,2]==1&&n[1,2]==n[2,1])} \\ M. F. Hasler, May 04 2015