A116486 Numbers k such that both k and k + 1 are logarithmically smooth.
8, 24, 80, 125, 224, 2400, 3024, 4224, 4374, 6655, 9800, 10647, 123200, 194480, 336140, 601425, 633555, 709631, 5142500, 5909760, 11859210, 1611308699
Offset: 1
Examples
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.
Links
- Discussion titled Special Smooth numbers, (postings in mersenneforum.org), starting March 20 2006.
Programs
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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 *)
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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 */
Extensions
Edited by Don Reble, Apr 07 2006
Comments