A261529 Number k such that k^2 + 1 = p*q*r where p,q,r are distinct primes and the sum p+q+r is a perfect square.

17, 37, 91, 235, 683, 1423, 1675, 2879, 8101, 9595, 13711, 18799, 19601, 21295, 25937, 30059, 32111, 36251, 39505, 41071, 49285, 60719, 79441, 90575, 93871, 94799, 103429, 112571, 132085, 136075, 144965, 180001, 180251, 188465, 189679

Offset

1,1

Comments

a(n) is odd. The prime numbers of the sequence are 17, 37, 683, 1423, 2879, 8101, 13711, 30059, 36251, 60719, 93871, 112571, 180001, ...

Links

Table of n, a(n) for n=1..35.

Example

17 is in the sequence because 17^2 + 1 = 2*5*29 and 2 + 5 + 29 = 6^2.

Maple

with(numtheory):
for n from 1 to 200000 do:
  y:=factorset(n^2+1):n0:=nops(y):
   if n0=3 and bigomega(n^2+1)=3 and
   sqrt(y[1]+y[2]+y[3])=floor(sqrt(y[1]+y[2]+y[3]))
   then
   printf(`%d, `, n):
   else
   fi:
od:

Prog

(PARI) isok(n) = my(f = factor(n^2+1)); (#f~ == 3) && (vecmax(f[, 2]) == 1) && issquare(vecsum(f[, 1])); \\ Michel Marcus, Aug 24 2015

Crossrefs

Cf. A002522, A180278.

Sequence in context: A048880 A075892 A155143 * A141886 A350096 A269240

Adjacent sequences: A261526 A261527 A261528 * A261530 A261531 A261532

Keyword

nonn

Author

Michel Lagneau, Aug 23 2015

Status

approved