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Odd numbers having odd numbers of prime factors, odd sums of prime factors and odd sums of decimal digits.
1

%I #6 Jan 09 2014 11:15:08

%S 3,5,7,23,27,29,41,43,47,61,67,83,89,113,131,137,139,151,157,173,179,

%T 191,193,195,197,199,223,227,229,241,243,263,269,281,283,285,311,313,

%U 317,331,337,353,357,359,373,379,397,399,401,409,421,429,443,449,461

%N Odd numbers having odd numbers of prime factors, odd sums of prime factors and odd sums of decimal digits.

%C A020639(a(n)), A001221(a(n)), A001222(a(n)), A008472(a(n)), A001414(a(n)) and A007953(a(n)) are all odd.

%H Harvey P. Dale, <a href="/A084424/b084424.txt">Table of n, a(n) for n = 1..1000</a>

%e 9675 is odd, 9675 = 3^2 * 5^2 * 43: omega=3, Omega=5, sopf=3+5+43=51, sopfr=3+3+5+5+43=59 and SumOfDigits=9+6+7+5=27, therefore 9675 is a term.

%t odQ[n_]:=And@@OddQ[{PrimeOmega[n],Total[IntegerDigits[n]],Total[ Transpose[ FactorInteger[n]][[1]]]}]; Select[Range[1,501,2],odQ] (* _Harvey P. Dale_, Jan 09 2014 *)

%K nonn,base

%O 1,1

%A _Reinhard Zumkeller_, Jun 27 2003