OFFSET
1,1
COMMENTS
N is logarithmically smooth if its largest prime factor p <= ceiling(log_2(n)).
Is the sequence finite?
No more terms with largest prime factor <= 47. - Joerg Arndt, Jul 02 2012
LINKS
Discussion titled Special Smooth numbers, (postings in mersenneforum.org), starting March 20 2006.
EXAMPLE
125 is in the sequence because 125 = 5 * 5 * 5, 126 = 2 * 3 * 3 * 7; no prime factor is greater than ceiling(log_2(125)) = 7.
MATHEMATICA
logCeilSmoothQ[n_, b_:E] := FactorInteger[n][[-1, 1]] <= Ceiling[Log[b, n]]; Select[Range[10000], logCeilSmoothQ[#, 2] && logCeilSmoothQ[# + 1, 2] &] (* Alonso del Arte, Nov 27 2019 *)
PROG
(PARI)
fm=97; /* max factor for factorizing, 2^97 >= searchlimit */
lpf(n)={ vecmax(factor(n, fm)[, 1]) } /* largest prime factor */
lsm(n)=if ( lpf(n)<=#binary(n-1), 1, 0 ); /* whether log-smooth, for n>=2 */
n0=3; /* lower search limit */
l1=lsm(n0-1);
{ for (n=n0, 10^10,
l0 = lsm(n);
if ( l0 && l1, print1(n-1, ", ") );
l1 = l0;
); }
/* Joerg Arndt, Jul 02 2012 */
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Harsh R. Aggarwal, Mar 20 2006
EXTENSIONS
Edited by Don Reble, Apr 07 2006
STATUS
approved