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 A006278 a(n) is the product of the first n primes congruent to 1 (mod 4). 15
 5, 65, 1105, 32045, 1185665, 48612265, 2576450045, 157163452745, 11472932050385, 1021090952484265, 99045822390973705, 10003628061488344205, 1090395458702229518345, 123214686833351935572985 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n)+2 is prime for n=1,2. No others are prime for n <= 200. Compare A002110 and A078586. - T. D. Noe, Dec 01 2002 Also, a(n) is least hypotenuse of exactly A003462(n) Pythagorean triangles of which 2^(n-1) are primitive. - Lekraj Beedassy, Dec 06 2003 Also, a(n) are the record setting values of m, for the number of solutions to "m*k-1 is a square", for some k, 1 <= k < m. There is one solution for m=2, and for a given m = a(n) there are 2^n solutions. For a given m there also 2^(n-1) solutions for primitively representing m as x^2 + y^2. See A008782. Also compare with A102476, which applies to "m*k+1 is a square". - Richard R. Forberg, Mar 18 2016 a(n) is the smallest m such that A000089(m) = 2^n. Also, numbers k for which A000089(k) sets a new record. - Jianing Song, Apr 27 2019 LINKS T. D. Noe, Table of n, a(n) for n = 1..100 Eric Weisstein's World of Mathematics, Pythagorean Triple FORMULA a(n) = Product_{i=1..n} A002144(i). - Alois P. Heinz, Mar 01 2021 MATHEMATICA maxN=15; pLst={}; k=0; While[Length[pLst] 0, AppendTo[result, {m, count}]], {m, 2, 1105}]; result  (* Richard R. Forberg, Mar 18 2016 *) PROG (PARI) tree(v)=my(t=#v); if(t<4, factorback(v), tree(v[1..t\2])*tree(v[t\2+1..t])); a(n, x=9*n\4+2)=my(P=select(p->p%4==1, primes(x))); if(#P

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Last modified May 17 19:26 EDT 2021. Contains 343988 sequences. (Running on oeis4.)