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
Keywords
Examples
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).
Links
- Amiram Eldar, Table of n, a(n) for n = 1..500
Crossrefs
Cf. A200070.
Programs
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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 *)