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 A192771 Numbers k such that k^2 + 1 is divisible by precisely five distinct primes where the sum of the largest and the smallest is equal to the sum of the other three. 3
 2153, 2697, 8487, 11293, 12553, 18065, 32247, 43999, 55945, 107607, 134223, 214641, 218783, 366937, 429855, 595471, 620865, 645327, 1330849, 1363977, 1387689, 1532465, 1557535, 1631191, 1716663, 1778711, 2156031, 3166415, 3857215, 4546071 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Amiram Eldar, Table of n, a(n) for n = 1..144 (terms below 10^9, terms 1..77 from Lukas Naatz) EXAMPLE 11293 is in the sequence because 11293^2+1 = 2 * 5 ^ 2 * 29 * 281 * 313 and 313 + 2 = 5 + 29 + 281 = 315. MAPLE isA192771 := proc(n) local p, s1, n2 ; n2 := n^2+1 ; if A001221(n2) = 5 then p := numtheory[factorset](n2) ; s1 := max(op(p)) + min( op(p)) ; evalb( add(k, k=p) = 2*s1 ) ; else false; end if; end proc: for n from 1 do if isA192771(n) then printf("%d, \n", n); end if; end do: # R. J. Mathar, Jul 11 2011 MATHEMATICA seqQ[n_] := Module[{p = FactorInteger[n^2 + 1][[;; , 1]]}, Length[p] == 5 && p[[1]] + p[[5]] == p[[2]] + p[[3]] + p[[4]]]; Select[Range[10^6], seqQ] (* Amiram Eldar, Jan 15 2020 *) PROG (PARI) for(k=1, 5000000, my(f=factor(k^2+1)); if(#f[, 2]==5, if(f[1, 1]+f[5, 1]==f[2, 1]+f[3, 1]+f[4, 1], print1(k, ", ")))) \\ Hugo Pfoertner, Jan 08 2020 CROSSREFS Cf. A180278, A192770. Sequence in context: A251846 A236150 A252126 * A152963 A179698 A075702 Adjacent sequences: A192768 A192769 A192770 * A192772 A192773 A192774 KEYWORD nonn AUTHOR Michel Lagneau, Jul 09 2011 EXTENSIONS a(17) and beyond from Lukas Naatz, Jan 08 2020 STATUS approved

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Last modified March 29 05:10 EDT 2023. Contains 361596 sequences. (Running on oeis4.)