

A145916


Even composites in A145832 with at least three distinct prime factors.


2



4346, 5246, 7124, 9434, 9698, 16826, 18422, 18814, 21826, 23084, 29606, 30806, 32570, 34844, 35294, 39614, 41534, 50060, 52646, 54164, 55574, 56234, 63110, 63554, 63626, 64076, 75206, 77654, 77774, 80954, 93716, 94604, 96134, 99644
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OFFSET

1,1


COMMENTS

Terms of A145915 that have at least three distinct prime factors. A145915 is the sequence of even composites in A145832. A145832 is the sequence of numbers n such that for each divisor d of n, k = d + n/d is squareroot smooth, i.e. p <= sqrt(k), where p is the largest prime dividing k.


LINKS

Klaus Brockhaus, Table of n, a(n) for n=1..4000
Eric Weisstein's World of Mathematics, Round Number


EXAMPLE

5246 = 2*43*61 is even and composite and has three distinct prime factors, 1, 2, 43, 61, 86, 122, 2623, 5246 are its divisors. 1+5246/1 = 5246+5246/5246 = 5247 = 3^2*11*53 and 53 < 72 < sqrt(5247); 2+5246/2 = 2623+5246/2623 = 2625 = 3*5^3*7 and 7 < 51 < sqrt(2625); 43+5246/43 = 122+5246/122 = 165 = 3*5^11 and 11 < 12 < sqrt(165); 61+5246/61 = 86+5246/86 = 147 = 3*7^2 and 7 < 12 < sqrt(147). Hence 5246 is in the sequence.


PROG

(MAGMA) [ n: n in [4..100000 by 2]  #PrimeDivisors(n) gt 2 and forall{ k: k in [ Integers()!(d+n/d): d in [ D[j]: j in [1..a] ] ]  k ge (IsEmpty(T) select 1 else Max(T) where T is [ x[1]: x in Factorization(k) ])^2 } where a is IsOdd(#D) select (#D+1)/2 else #D/2 where D is Divisors(n) ];


CROSSREFS

Cf. A145832, A048098 (squareroot smooth numbers), A145915.
Sequence in context: A259961 A252431 A251947 * A048900 A294985 A252302
Adjacent sequences: A145913 A145914 A145915 * A145917 A145918 A145919


KEYWORD

nonn


AUTHOR

Klaus Brockhaus, Oct 26 2008


STATUS

approved



