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 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 (list; graph; refs; listen; history; text; internal format)
 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 square-root 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: 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 (square-root 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

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Last modified August 19 15:27 EDT 2022. Contains 356229 sequences. (Running on oeis4.)