A228182 a(n) is the smallest k such that the sum of squares of prime divisors of k is equal to the sum of prime divisors of n+k.

12, 810, 35152, 18, 9, 67881, 6, 36, 20, 12, 3, 7203, 14688, 162, 350, 6, 81, 75, 9, 24, 25, 3648, 37905, 2125, 3, 18, 455, 225, 27, 3800, 81, 12, 343, 54, 26730, 1540, 180, 6, 14, 48, 5, 10010, 96348, 798, 49, 360, 9, 45, 3430, 192, 126, 36, 3, 225, 729, 648

Offset: 1

Author

Michel Lagneau, Aug 15 2013

Keywords

• nonn

Comments

Smallest k such that A005063(k) = A008472(n+k), where A008472(n) is the sum of the distinct primes dividing n and A005063(n) is the sum of squares of primes dividing n.

Examples

			a(2) = 810 because the prime divisors of 810 are {2, 3, 5}, the prime divisors of 810 + 2 = 812 are {2, 7, 29} and 2^2 + 3^2 + 5^2 = 2 + 7 + 29 = 38, hence 810 is in the sequence.
		

Crossrefs

Cf. A005063, A008472, A228181.

Programs

Mathematica

sk[n_]:=Module[{k=1},While[Plus@@(First@#&/@FactorInteger[k]^2)!=Plus@@(First@#&/@FactorInteger[n+k]),k++];k];Array[sk,65,1]