A163836 Composites whose largest prime factor is equal to the sum of all the other prime factors (with repetition).

4, 9, 25, 30, 49, 70, 84, 121, 169, 286, 289, 308, 361, 440, 495, 528, 529, 594, 646, 728, 819, 841, 884, 961, 975, 1040, 1170, 1248, 1369, 1404, 1496, 1681, 1683, 1748, 1798, 1849, 1976, 2209, 2223, 2499, 2809, 2975, 3128, 3135, 3344, 3481, 3519, 3526, 3570

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 05 2009

Keywords

• nonn

Comments

Sequence contains the square of every prime. - Sean A. Irvine, Oct 05 2009

Contains 4*A143206. - David A. Corneth, Apr 28 2020

Contains 2*A037074. - Bernard Schott, Apr 28 2020

Examples

			a(1) = 4 (2=2), a(2) = 9 (3=3), a(3) = 25 (5=5), a(4) = 30 (5=3+2), a(5) = 49 (7=7), a(6) = 70 (7=5+2), a(7) = 84 (7=3+2+2), a(8) = 121 (11=11), a(9) = 169 (13=13), a(10) = 286 (13=11+2), a(11) = 289(17=17), a(12) = 308 (11=7+2+2), ...
		

Links

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

Crossrefs

Cf. A002808, A037074, A143206.

Programs

Maple

A002808 := proc(n) option remember; local a; if n = 1 then 4; else for a from procname(n-1)+1 do if not isprime(a) then return a; end if; end do: end if; end proc: A006530 := proc(n) if n = 1 then 1; else numtheory[factorset](n) ; max(op(%)) ; end if; end: A001414 := proc(n) ifactors(n)[2] ; add( op(1,p)*op(2,p),p=%) ; end: A163836 := proc(n) option remember; local a,lpf; if n =1 then 4; else for a from procname(n-1)+1 do if not isprime(a) then lpf := A006530(a) ; if 2*lpf = A001414(a) then return a; end if; end if; od: end if; end: seq(A163836(n),n=1..80) ; # R. J. Mathar, Oct 10 2009

Mathematica

seqQ[n_] := Module[{f = FactorInteger[n]}, If[Length[f] == 1, f[[1, 2]] == 2, f[[-1, 2]] == 1 && f[[-1, 1]] == Plus @@ Times @@@ Most[f]]]; Select[Range[4000], seqQ] (* Amiram Eldar, Apr 28 2020 *)

Python

from sympy import factorint
def ok(n):
  f = factorint(n)
  return sum(f[p] for p in f) > 1 and 2*max(f) == sum(p*f[p] for p in f)
print(list(filter(ok, range(3571)))) # Michael S. Branicky, Apr 09 2021

Extensions

Corrected and extended by Sean A. Irvine and R. J. Mathar, Oct 05 2009