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A192770 Numbers k such that k^2 + 1 is divisible by precisely four distinct primes where the sum of the largest and the smallest is equal to the sum of the other two. 3
948, 1560, 1772, 13236, 36984, 40452, 94536, 100512, 127224, 425808, 757382, 850416, 875784, 1241106, 2102736, 3343164, 4361808, 4530480, 5401464, 8006700, 8645004, 9806604, 10379136, 10829580, 11366424, 11692746, 13960260 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..80 (terms below 10^9)

EXAMPLE

1772 is in the sequence because 1772^2+1 = 5 * 17^2 * 41 * 53 and 5 + 53 = 17 + 41.

MAPLE

with(numtheory):for n from 1 to 100000 do:x:=n^2+1:y:=factorset(x):n1:=nops(y):if n1=4 and y[4] + y[1] = y[2]+y[3] then printf ( "%d %d \n", n, x):else fi:od:

MATHEMATICA

seqQ[n_] := Module[{p = FactorInteger[n^2 + 1][[;; , 1]]}, Length[p] == 4 && p[[1]] + p[[4]] == p[[2]] + p[[3]]]; Select[Range[10^6], seqQ] (* Amiram Eldar, Jan 15 2020 *)

PROG

(PARI) is(n)=my(f=factor(n^2+1)[, 1]); #f==4&&f[1]+f[4]==f[2]+f[3]

forstep(n=2, 1e7, 2, if(is(n), print1(n", "))) \\ Charles R Greathouse IV, Jul 11 2011

CROSSREFS

Cf. A180278, A192771.

Sequence in context: A248785 A199924 A215950 * A187627 A170830 A020366

Adjacent sequences:  A192767 A192768 A192769 * A192771 A192772 A192773

KEYWORD

nonn

AUTHOR

Michel Lagneau, Jul 09 2011

EXTENSIONS

a(10)-a(27) from Charles R Greathouse IV, Jul 11 2011

STATUS

approved

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Last modified October 27 18:16 EDT 2021. Contains 348287 sequences. (Running on oeis4.)