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Nonnegative integers k such that Sum_{d|k} k & (k/d) is an odd prime, where & is the bitwise AND operator.
2

%I #12 Sep 08 2022 08:46:24

%S 9,25,81,121,289,625,729,841,1681,3249,3481,5041,7225,8281,8649,9025,

%T 10201,11449,13689,15129,18769,19881,22201,25281,27225,28561,29241,

%U 31329,32041,33489,34225,36481,38025,38809,42849,46225,48841,51529,53361,55225,56169,57121

%N Nonnegative integers k such that Sum_{d|k} k & (k/d) is an odd prime, where & is the bitwise AND operator.

%C A subsequence of the odd squares A016754.

%p select(k -> (A327987(k) <> 2 and isprime(A327987(k))), [$0..60000]);

%o (Magma) [k:k in [1..60000]|IsOdd(a) and IsPrime(a) where a is &+[BitwiseAnd(d,k div d):d in Divisors(k)]]; // _Marius A. Burtea_, Oct 11 2019

%Y Cf. A327987, A327988, A016754.

%K nonn

%O 1,1

%A _Peter Luschny_, Oct 11 2019