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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A048880 A075892 A155143 * A141886 A350096 A269240
KEYWORD
nonn
AUTHOR
Michel Lagneau, Aug 23 2015
STATUS
approved

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Last modified July 21 06:08 EDT 2024. Contains 374463 sequences. (Running on oeis4.)