

A145915


Even composites in A145832.


1



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
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OFFSET

1,1


COMMENTS

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

Table of n, a(n) for n=1..43.
Eric Weisstein's World of Mathematics, Round Number


EXAMPLE

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.


PROG

(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) ];


CROSSREFS

Cf. A145832, A048098 (squareroot smooth numbers), A145916.
Sequence in context: A124969 A294594 A031510 * A248406 A135666 A119379
Adjacent sequences: A145912 A145913 A145914 * A145916 A145917 A145918


KEYWORD

nonn


AUTHOR

Klaus Brockhaus, Oct 26 2008


STATUS

approved



