A212862 Numbers k such that the sum of prime factors of k (counted with multiplicity) equals four times the largest prime divisor of k.

16, 72, 81, 625, 750, 800, 900, 960, 1080, 1215, 2401, 3430, 4116, 4900, 5880, 6272, 6615, 7000, 7056, 7875, 7938, 8400, 8960, 9450, 10080, 10752, 11340, 12096, 13608, 14641, 15309, 28561, 37268, 48334, 53240, 59895, 63888, 71874, 81796, 83521, 88935, 94864

Offset: 1

Author

Michel Lagneau, May 29 2012

Keywords

• nonn

Comments

The numbers prime(n)^4 are in the sequence.

Examples

			750 is in the sequence because 750 = 2*3*5^3 => sum of prime divisors = 2+3 + 5*3 = 20 = 4*5 where 5 is the greatest prime divisor.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001414, A163836, A212861.

Programs

Maple

with(numtheory):A:= proc(n) local e, j; e := ifactors(n)[2]: add (e[j][1]*e[j][2], j=1..nops(e)) end: for m from 2 to 100000 do: x:=factorset(m):n1:=nops(x):if A(m)=4*x[n1] then printf(`%d, `,m):else fi:od:

Mathematica

Select[Range[2, 10^5], Plus @@ Times @@@ (f = FactorInteger[#]) == 4 * f[[-1, 1]] &] (* Amiram Eldar, Apr 24 2020 *)