A145832 -id:A145832 - cp's OEIS frontend

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

Klaus Brockhaus, Oct 26 2008

nonn

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.

			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.

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

Cf. A145832, A048098 (square-root smooth numbers), A145915.

[ 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) ];

A145915 Even composites in A145832.

Original entry on oeis.org

146, 164, 458, 524, 584, 626, 764, 956, 1084, 1172, 1322, 1478, 1858, 1934, 2138, 2174, 2336, 2966, 3158, 3464, 3548, 3566, 3884, 3974, 3998, 4124, 4274, 4346, 4696, 5042, 5102, 5246, 5354, 5414, 6002, 6038, 6434, 6626, 6646, 6782, 6884, 7034, 7094

Offset: 1

Klaus Brockhaus, Oct 26 2008

nonn

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.

			146 = 2*73 is even and composite, 1, 2, 73, 146 are its divisors. 1+146/1 = 146+146/146 = 147 = 3*7^2 and 7 < 12 < sqrt(147); 2+146/2 = 73+146/73 = 75 = 3*5^2 and 5 < 8 < sqrt(75). Hence 146 is in the sequence.

Eric Weisstein's World of Mathematics, Round Number

Cf. A145832, A048098 (square-root smooth numbers), A145916.

[ n: n in [4..7100 by 2] | 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) ];

cp's OEIS Frontend

A145916 Even composites in A145832 with at least three distinct prime factors.

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