A228436 - OEIS

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

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OFFSET

1,2

COMMENTS

A multiplicative analog of A231271.

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

LINKS

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

EXAMPLE

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.

MATHEMATICA

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 *)

PROG

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

CROSSREFS

Cf. A231271, A000069, A001969.

Sequence in context: A194440 A220520 A330165 * A189364 A022797 A190884

Adjacent sequences: A228433 A228434 A228435 * A228437 A228438 A228439

KEYWORD

nonn,base

AUTHOR

Vladimir Shevelev, Nov 10 2013

EXTENSIONS

More terms from Michel Marcus

STATUS

approved