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.

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

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