A231271 -id:A231271 - cp's OEIS frontend

A228436 Odd n such that n*d are both odious (A000069) or both evil (A001969) for every divisor d of n.

1, 3, 7, 11, 15, 19, 31, 41, 53, 59, 63, 67, 79, 83, 91, 97, 103, 105, 117, 127, 131, 141, 157, 167, 173, 179, 181, 185, 193, 217, 219, 223, 227, 229, 237, 239, 251, 255, 269, 271, 277, 281, 283, 291, 293, 303, 307, 311, 313, 317, 337, 347, 351, 359, 377

Offset: 1

Vladimir Shevelev, Nov 10 2013

A multiplicative analog of A231271.

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

			Evil number n=15 has divisors {1,3,5,15}.
Since all numbers 15*1=15, 15*3=45, 15*5=75 and 15*15=225 are evil, then 15 is a term.

Peter J. C. Moses, Table of n, a(n) for n = 1..5000

Cf. A231271, A000069, A001969.

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 *)

isok(n) = (n % 2) && (!(s = sumdiv(n, d, hammingweight(n*d) % 2)) || (s == numdiv(n))); \\ Michel Marcus, Nov 10 2013

More terms from Michel Marcus

A231558 Odd composite numbers n, such that n, n+d, n*d and n/d are all odious (A000069) for every divisor d of n.

Original entry on oeis.org

217, 511, 889, 949, 1957, 2041, 2263, 2413, 2869, 3113, 3133, 3481, 3991, 5201, 5761, 7813, 7903, 8071, 8137, 8773, 10519, 10609, 11377, 11879, 12191, 12313, 12871, 15127, 15223, 16177, 19561, 19733, 19879, 21151, 23077, 23233, 23449, 23573, 26221, 27469

Offset: 1

Vladimir Shevelev and Peter J. C. Moses, Nov 11 2013

All terms are in A079523.

			Let n=217. Its divisors are {1,7,31,217}. We see that all numbers 217+1=218, 217+7=224, 217+31=248, 217+217=434, 217/1=217, 217/7=31, 217/31=7, 217/217=1, 217*1=217, 217*7=1519, 217*31=6727, 217*217=47089 are odious. Thus 217 is in the sequence.

Peter J. C. Moses, Table of n, a(n) for n = 1..10000

Cf. A231271, A228436, A000069, A079523.

cp's OEIS Frontend

A228436 Odd n such that n*d are both odious (A000069) or both evil (A001969) for every divisor d of n.

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