A200071 Numbers n such that the sum of the prime distinct divisors of n^2+1 equals 2 times the difference between the largest and the smallest prime divisor.

447, 2042, 4942, 8673, 17232, 18321, 38232, 52953, 54468, 54974, 55174, 57229, 66567, 71132, 83071, 101499, 113667, 121206, 133047, 173932, 297907, 325286, 430353, 447131, 656079, 702969, 842151, 937313, 1061846, 1173886, 1613346, 1721094, 1754679, 1759310

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..500

Example

447 is a term because the distinct prime divisors of 447^2 + 1 are 2, 5, 13, 29, 53 and their sum, 2 + 5 + 13 + 29 + 53 = 102, equals 2*(53 - 2).

Mathematica

Select[Range[1800000], Plus@@(pl=First/@FactorInteger[#^2+1])/2==pl[[-1]]-pl[[1]]&]
spddQ[n_]:=Module[{fi=FactorInteger[n^2+1][[All, 1]]}, Total[fi] == 2*(Last[ fi]-First[fi])]; Select[Range[176*10^4], spddQ] (* Harvey P. Dale, Jan 12 2019 *)

Crossrefs

Cf. A200070.

Sequence in context: A139230 A221506 A065576 * A203960 A147628 A153486

Adjacent sequences: A200068 A200069 A200070 * A200072 A200073 A200074

Keyword

nonn

Author

Michel Lagneau, Nov 13 2011

Status

approved