A145916 Even composites in A145832 with at least three distinct prime factors.
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
Offset: 1
Keywords
Examples
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.
Links
- Klaus Brockhaus, Table of n, a(n) for n=1..4000
- Eric Weisstein's World of Mathematics, Round Number
Programs
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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) ];
Comments