A071639 Numbers k such that core(k) = b(k,1)*b(k,0) where b(k,1) is the number of 1's in binary representation of k, b(k,0) the number of 0's and core(k) the squarefree part of k.

24, 3500, 6048, 52855, 56320, 67270, 71874, 80920, 85536, 95830, 105600, 112000, 117670, 131625, 142373, 155925, 250173, 262392, 280800, 350142, 360672, 673036, 965419, 984256, 1041859, 1078110, 1144440, 1166990, 1283040, 1331000, 1355310, 1454750, 1480160, 1691360

Offset: 1

Author

Benoit Cloitre, Jun 22 2002

Keywords

• easy
• nonn
• base

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007913, A071295.

Programs

Mathematica

core[n_] := Times @@ (First[#]^Mod[Last[#], 2]& /@ FactorInteger[n]); b[n_] := Times @@ DigitCount[n, 2, {0, 1}]; Select[Range[10^5], core[#] == b[#] &] (* Amiram Eldar, Sep 03 2020 *)

PARI

for(s=1,500000,b=binary(s); l=length(b); if(sum(i=1,l,if(component(b,i)-1,0,1))*sum(i=1,l,if(component(b,i),0,1))==core(s),print1(s,",")))

Extensions

More terms from Amiram Eldar, Sep 03 2020