OFFSET
1,1
COMMENTS
It seems that n is the product of twin primes of A232878 for n > 3.
Conjecture: the numbers n such that for any positive integers (a, b), a * b = n and a + b is a square are the product of twin primes, and a*b+1 is also a perfect square.
LINKS
Hiroaki Yamanouchi, Table of n, a(n) for n = 1..1163
EXAMPLE
323 is the product of two positive integers in 2 ways: 1 * 323 and 17 * 19. The sums of the pairs of multiplicands are 323+1 = 18^2 and 17+19 = 6^2 respectively. All are squares.
MATHEMATICA
t={}; Do[ds=Divisors[n]; If[EvenQ[Length[ds]], ok=True; k=1; While[k<=Length[ds]/2 && (ok=IntegerQ[Sqrt[ds[[k]]+ds[[ -k]]]]), k++ ]; If[ok, AppendTo[t, n]]], {n, 2, 10^8}]; t ***[Program from T.D. Noe adapted for this sequence. See A080715]***
PROG
(PARI) isok(n) = {d = divisors(n); if (#d % 2, return (0)); for (i = 1, #d/2, if (! issquare(d[i]+n/d[i]), return (0)); ); return (1); } \\ Michel Marcus, Jan 06 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jan 06 2014
EXTENSIONS
a(21)-a(23) from Hiroaki Yamanouchi, Oct 02 2014
STATUS
approved