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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 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

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