A228436 - OEIS

%I #15 Nov 12 2013 15:47:13

%S 1,3,7,11,15,19,31,41,53,59,63,67,79,83,91,97,103,105,117,127,131,141,

%T 157,167,173,179,181,185,193,217,219,223,227,229,237,239,251,255,269,

%U 271,277,281,283,291,293,303,307,311,313,317,337,347,351,359,377

%N Odd n such that n*d are both odious (A000069) or both evil (A001969) for every divisor d of n.

%C A multiplicative analog of A231271.

%C A prime p is a term, iff p and p^2 are both odious or both evil.

%H Peter J. C. Moses, <a href="/A228436/b228436.txt">Table of n, a(n) for n = 1..5000</a>

%e Evil number n=15 has divisors {1,3,5,15}.

%e Since all numbers 15*1=15, 15*3=45, 15*5=75 and 15*15=225 are evil, then 15 is a term.

%t odiousQ[n_]:=OddQ[DigitCount[n,2][[1]]]; selQ[n_]:=OddQ[n] && Length[Union[Map[odiousQ, Map[n #&,Divisors[n]]]]] == 1; Select[Range[400], selQ] (* _Peter J. C. Moses_, Nov 10 2013 *)

%o (PARI) isok(n) = (n % 2) && (!(s = sumdiv(n, d, hammingweight(n*d) % 2)) || (s == numdiv(n))); \\ _Michel Marcus_, Nov 10 2013

%Y Cf. A231271, A000069, A001969.

%K nonn,base

%O 1,2

%A _Vladimir Shevelev_, Nov 10 2013

%E More terms from _Michel Marcus_