Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #16 Aug 24 2015 04:11:58
%S 17,37,91,235,683,1423,1675,2879,8101,9595,13711,18799,19601,21295,
%T 25937,30059,32111,36251,39505,41071,49285,60719,79441,90575,93871,
%U 94799,103429,112571,132085,136075,144965,180001,180251,188465,189679
%N 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.
%C a(n) is odd. The prime numbers of the sequence are 17, 37, 683, 1423, 2879, 8101, 13711, 30059, 36251, 60719, 93871, 112571, 180001, ...
%e 17 is in the sequence because 17^2 + 1 = 2*5*29 and 2 + 5 + 29 = 6^2.
%p with(numtheory):
%p for n from 1 to 200000 do:
%p y:=factorset(n^2+1):n0:=nops(y):
%p if n0=3 and bigomega(n^2+1)=3 and
%p sqrt(y[1]+y[2]+y[3])=floor(sqrt(y[1]+y[2]+y[3]))
%p then
%p printf(`%d, `,n):
%p else
%p fi:
%p od:
%o (PARI) isok(n) = my(f = factor(n^2+1)); (#f~ == 3) && (vecmax(f[,2]) == 1) && issquare(vecsum(f[,1])); \\ _Michel Marcus_, Aug 24 2015
%Y Cf. A002522, A180278.
%K nonn
%O 1,1
%A _Michel Lagneau_, Aug 23 2015