A242455 Numbers are the product of k primes: prime(n_1)...prime(n_k), where prime(x) is the x-th prime. This is a list of maximal numbers given k and the sum n_1+n_2+...+n_k.

2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 19, 20, 23, 24, 25, 29, 30, 31, 32, 35, 37, 40, 41, 43, 47, 48, 50, 53, 55, 59, 60, 61, 64, 67, 71, 73, 75, 77, 79, 80, 83, 89, 96, 97, 100, 101, 103, 107, 109, 113, 120, 121, 125, 127, 128, 131, 137, 139, 143

Offset

1,1

Comments

All primes are in the sequence. - Michel Marcus, May 23 2014

All powers of 2 are in the sequence. 3*2^n is in the sequence.

3^n and 7^n and 13^n not in the sequence for n > 1. - Gordon Hamilton, May 24 2014

Links

Table of n, a(n) for n=1..63.

Example

For k = 3 and the sum n_1 + n_2 + n_3 = 7; the numbers 42 = prime(1)*prime(2)*prime(4) and 45 = prime(2)*prime(2)*prime(3) are not in the list because 50 = prime(1)*prime(3)*prime(3) is a larger number which satisfies the constraints.
For k = 2 and the sum n_1 + n_2 = 18; prime(9)*prime(9) = 23*23 = 529 is not on the list because prime(8)*prime(10) = 19*29 = 551 is larger.

Prog

(PARI) nbk(f) = sum(i=1, #f~, f[i, 2]*primepi(f[i, 1]));
snk(f) = sum(i=1, #f~, f[i, 2]);
value(digs) = prod(i=1, #digs, if (digs[i], prime(digs[i]), 1));
isok(n) = {f = factor(n); k = nbk(f); sk = snk(f); if (sk == 1, return (1)); for (j=k^(sk-1)+1, k^sk-1, dibk = digits(j, k); val = value(dibk); fv = factor(val); kv = nbk(fv); skv = snk(fv); if ((kv == k) && (skv == sk), if (val > n, return (0); ); ); ); return (1); } \\ Michel Marcus, May 23 2014

Crossrefs

Sequence in context: A066522 A193159 A308018 * A339879 A274374 A007298

Adjacent sequences: A242452 A242453 A242454 * A242456 A242457 A242458

Keyword

nonn

Author

Gordon Hamilton, May 14 2014

Extensions

More terms from Michel Marcus, May 23 2014

Status

approved