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

1,1

Comments

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

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A000961, A005063, A008472, A164722.

Sequence in context: A069550 A079705 A068721 * A196208 A196475 A253534

Adjacent sequences: A228178 A228179 A228180 * A228182 A228183 A228184

Keyword

nonn

Author

Michel Lagneau, Aug 15 2013

Status

approved