A145915 Even composites in A145832.

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

Author

Klaus Brockhaus, Oct 26 2008

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Round Number

Crossrefs

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

Programs

Magma

[ 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) ];