OFFSET
1,1
COMMENTS
A necessary condition is that the number be one less than a round number; if this number is prime it's in the sequence.
Even composites in this sequence seem rare (see examples below for more details).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Round Number
EXAMPLE
The first term is a prime one less than the round number 4.
The first composite number in this sequence is 15, with divisor-pair sum 3+5 = 8.
Another such composite is 63, with divisor-pair sums: 3+21 = 24, 7+9 = 16.
There are only five even composites among the first 100 terms of this sequence.
The first such is 146, with divisor-pair sum 2+73 = 75. The second is 164, with divisor-pair sums 2+82 = 84 and 4+41 = 45. The remaining three are 458, 524 and 584.
MATHEMATICA
smQ[n_] := FactorInteger[n][[-1, 1]]^2 <= n; seqQ[n_] := AllTrue[Divisors[n], smQ[# + n/#] &]; Select[Range[320], seqQ] (* Amiram Eldar, Jun 13 2020 *)
PROG
(Magma) [ n: n in [1..310] | 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) ]; // Klaus Brockhaus, Oct 24 2008
CROSSREFS
KEYWORD
nonn
AUTHOR
Dan Sonnenschein (dans(AT)portal.ca), Oct 20 2008
EXTENSIONS
Wrong term 305 removed by Amiram Eldar, Jun 13 2020
STATUS
approved