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

1,1

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A001414, A163836, A212861.

Sequence in context: A264888 A272964 A232579 * A253151 A339993 A232402

Adjacent sequences: A212859 A212860 A212861 * A212863 A212864 A212865

Keyword

nonn

Author

Michel Lagneau, May 29 2012

Status

approved