A228181 Numbers k such that sum of square of prime divisors of k equals sum of prime divisors of k+1.

12, 27, 385, 1120, 4840, 9936, 14500, 29440, 95795, 105875, 178904, 223155, 341248, 343343, 754985, 830908, 1059630, 1841049, 2408832, 2949375, 3564704, 4934358, 5368792, 5500312, 6695000, 6805372, 8332831, 8846656, 10126336, 12956040, 13157235, 17254600

Offset: 1

Author

Michel Lagneau, Aug 15 2013

Keywords

• nonn

Comments

Numbers k such that A005063(k) = A008472(k+1).

Examples

			The prime divisors of 9936 are {2, 3, 23} and the prime divisors of 9937 are {19, 523} => 2^2 + 3^2 + 23^2 = 19 + 523 = 542, hence 9936 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..333 (terms below 10^10)

Crossrefs

Cf. A000961, A005063, A008472, A164722.

Programs

Magma

[k:k in [2..2500000]| &+PrimeDivisors(k+1) eq &+[PrimeDivisors(k)[i]^2: i in [1..#PrimeDivisors(k)]]]; // Marius A. Burtea, Feb 18 2020

Mathematica

fQ[n_] := Plus @@ (First@# & /@ FactorInteger[n]^2) == Plus @@ (First@# & /@ FactorInteger[n + 1]); Select[ Range@ 100000, fQ]