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

1,1

Comments

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

Links

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

Example

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.

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]<n, [$4..N]):
map(proc(n) if Lpf[n]=Lpf[comps[n]] then comps[n] fi end proc,
[$1..nops(comps)]); # 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 *)

Crossrefs

Cf. A002808, A050696.

Sequence in context: A116612 A068502 A109959 * A218335 A030591 A343598

Adjacent sequences: A161987 A161988 A161989 * A161991 A161992 A161993

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jun 24 2009

Extensions

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

Status

approved