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A154373 Composites k such that gpf(k) - lpf(k) is an odd nonprime. 1

%I

%S 6,12,18,22,24,34,36,44,46,48,54,58,66,68,72,74,82,88,92,94,96,102,

%T 106,108,110,116,118,132,134,136,138,142,144,148,154,158,162,164,166,

%U 170,174,176,178,184,188,192,194,198,202,204,212,214,216,220,222,226,230

%N Composites k such that gpf(k) - lpf(k) is an odd nonprime.

%H Harvey P. Dale, <a href="/A154373/b154373.txt">Table of n, a(n) for n = 1..1000</a>

%e 6 = 3*2 and 3 - 2 = 1 (odd nonprime), so 6 is a term;

%e 12 = 3*2*2 and 3 - 2 = 1 (odd nonprime), so 12 is a term;

%e 18 = 3*3*2 and 3 - 2 = 1 (odd nonprime), so 18 is a term;

%e 22 = 11*2 and 11 - 2 = 9 (odd nonprime), so 22 is a term.

%p A020639 := proc(n) numtheory[factorset](n) ; min(op(%)) ; end proc:

%p A006530 := proc(n) numtheory[factorset](n) ; max(op(%)) ; end proc:

%p for n from 1 to 500 do c := A006530(A002808(n)) - A020639(A002808(n)) ; if type(c,'odd') and not isprime(c) then printf("%d,",A002808(n) ) ; end if; end do: # _R. J. Mathar_, May 05 2010

%t lpfQ[n_]:=Module[{fi=Transpose[FactorInteger[n]][[1]],c},c= Last[fi]-First[fi]; OddQ[c]&&!PrimeQ[c]]; Select[Range[300],lpfQ] (* _Harvey P. Dale_, Nov 25 2012 *)

%Y Cf. A002808 (composites), A141468 (odd nonprimes).

%Y Cf. A006530 (gpf), A020639 (lpf).

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Jan 08 2009

%E Corrected (69 replaced by 68, 203 removed) by _R. J. Mathar_, May 05 2010

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Last modified December 5 16:12 EST 2019. Contains 329753 sequences. (Running on oeis4.)