cp's OEIS Frontend

A372591 Numbers whose binary weight (A000120) plus bigomega (A001222) is even.

%I A372591 #6 May 15 2024 16:28:46
%S A372591 2,6,7,8,9,10,11,13,15,19,24,28,31,32,33,34,36,37,39,40,41,42,44,46,
%T A372591 47,50,51,52,54,57,58,59,60,61,65,67,70,73,76,77,79,85,86,90,95,96,97,
%U A372591 98,103,106,107,109,110,111,112,117,119,123,124,126,127,128,129
%N A372591 Numbers whose binary weight (A000120) plus bigomega (A001222) is even.
%C A372591 The odd version is A372590.
%e A372591 The terms (center), their binary indices (left), and their weakly decreasing prime indices (right) begin:
%e A372591           {2}   2  (1)
%e A372591         {2,3}   6  (2,1)
%e A372591       {1,2,3}   7  (4)
%e A372591           {4}   8  (1,1,1)
%e A372591         {1,4}   9  (2,2)
%e A372591         {2,4}  10  (3,1)
%e A372591       {1,2,4}  11  (5)
%e A372591       {1,3,4}  13  (6)
%e A372591     {1,2,3,4}  15  (3,2)
%e A372591       {1,2,5}  19  (8)
%e A372591         {4,5}  24  (2,1,1,1)
%e A372591       {3,4,5}  28  (4,1,1)
%e A372591   {1,2,3,4,5}  31  (11)
%e A372591           {6}  32  (1,1,1,1,1)
%e A372591         {1,6}  33  (5,2)
%e A372591         {2,6}  34  (7,1)
%e A372591         {3,6}  36  (2,2,1,1)
%e A372591       {1,3,6}  37  (12)
%e A372591     {1,2,3,6}  39  (6,2)
%e A372591         {4,6}  40  (3,1,1,1)
%e A372591       {1,4,6}  41  (13)
%e A372591       {2,4,6}  42  (4,2,1)
%t A372591 Select[Range[100],EvenQ[DigitCount[#,2,1]+PrimeOmega[#]]&]
%Y A372591 For sum (A372428, zeros A372427) we have A372587, complement A372586.
%Y A372591 For minimum (A372437) we have A372440, complement A372439.
%Y A372591 Positions of even terms in A372441, zeros A071814.
%Y A372591 For maximum (A372442, zeros A372436) we have A372589, complement A372588.
%Y A372591 The complement is A372590.
%Y A372591 For just binary indices:
%Y A372591 - length: A001969, complement A000069
%Y A372591 - sum: A158704, complement A158705
%Y A372591 - minimum:  A036554, complement A003159
%Y A372591 - maximum: A053754, complement A053738
%Y A372591 For just prime indices:
%Y A372591 - length: A026424 A028260 (count A027187), complement (count A027193)
%Y A372591 - sum: A300061 (count A058696), complement A300063 (count A058695)
%Y A372591 - minimum: A340933 (count A026805), complement A340932 (count A026804)
%Y A372591 - maximum: A244990 (count A027187), complement A244991 (count A027193)
%Y A372591 A019565 gives Heinz number of binary indices, adjoint A048675.
%Y A372591 A029837 gives greatest binary index, least A001511.
%Y A372591 A031215 lists even-indexed primes, odd A031368.
%Y A372591 A048793 lists binary indices, length A000120, reverse A272020, sum A029931.
%Y A372591 A070939 gives length of binary expansion.
%Y A372591 A112798 lists prime indices, length A001222, reverse A296150, sum A056239.
%Y A372591 Cf. A000720, A006141, A066207, A257991, A300272, A304818, A340604, A341446, A372429-A372433, A372438.
%K A372591 nonn
%O A372591 1,1
%A A372591 _Gus Wiseman_, May 14 2024