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

1,1

Links

Table of n, a(n) for n=1..37.

Example

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

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 *)

Prog

(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();
(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

Crossrefs

Cf. some subsequences: A079704, A104126.

Sequence in context: A199989 A201056 A352081 * A190508 A298161 A195419

Adjacent sequences: A257401 A257402 A257403 * A257405 A257406 A257407

Keyword

nonn

Author

William Brian Repko, Apr 22 2015

Status

approved