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

1,1

Links

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

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 *)

Prog

(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, ", ")))

Crossrefs

Cf. A007913, A071295.

Sequence in context: A349115 A159681 A275569 * A061530 A275637 A223123

Adjacent sequences: A071636 A071637 A071638 * A071640 A071641 A071642

Keyword

easy,nonn,base

Author

Benoit Cloitre, Jun 22 2002

Extensions

More terms from Amiram Eldar, Sep 03 2020

Status

approved