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
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
KEYWORD
nonn
AUTHOR
Gordon Hamilton, May 14 2014
EXTENSIONS
More terms from Michel Marcus, May 23 2014
STATUS
approved