A161990 Composites which have the same largest prime factor as their index.

10, 12, 14, 25, 36, 39, 42, 45, 77, 124, 132, 140, 147, 224, 234, 266, 345, 365, 370, 375, 380, 385, 390, 494, 621, 638, 660, 671, 682, 782, 899, 945, 1001, 1086, 1140, 1377, 1558, 1577, 1628, 1696, 1728, 1760, 1798, 1885, 2046, 2145, 2484, 2550, 2970, 3101, 3122, 3477

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 24 2009

Keywords

• nonn

Comments

If A052369(k) = A006530(k), we add the associated composite A002808(k) to the sequence.

Examples

			The 6th composite is 12=2^2*3 with largest prime factor 3, and the largest prime factor of the index 6=2*3 is also 3, which adds 12 to the sequence.
The 7th composite is 14=2*7 with largest prime factor 7, and the largest prime factor of the index 7 is also 7, which adds 14 to the sequence.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..4262

Crossrefs

Cf. A002808, A050696.

Programs

Maple

A006530 := proc(n) sort(convert(numtheory[factorset](n),list)); op(-1,%) ; end:
A002808 := proc(n) if n = 1 then 4; else for a from procname(n-1)+1 do if not isprime(a) then RETURN(a) ; fi; od: fi; end:
A052369 := proc(n) A006530(A002808(n)) ; end:
for n from 1 to 10000 do if A052369(n) = A006530(n) then printf("%d,",A002808(n)) ; fi; od: # R. J. Mathar, Aug 14 2009
# More efficient alternative:
N:= 10000: # to get terms <= N
Lpf:= [seq(max(numtheory:-factorset(n)),n=1..N)]:
comps:= select(n -> Lpf[n]Robert Israel, Mar 05 2018

Mathematica

lpf[n_] := FactorInteger[n ][[-1, 1]];
cc = Select[Range[10000], CompositeQ];
Select[{Range[Length[cc]], cc} // Transpose, lpf[#[[1]]] == lpf[#[[2]]]&][[All, 2]] (* Jean-François Alcover, Aug 19 2020 *)

Extensions

Corrected and extended by R. J. Mathar, Aug 14 2009