A324718 Odd numbers n for which bitand(2n,sigma(n)) = 2*bitand(n,sigma(n)-n), where bitand is bitwise-AND, A004198.

1, 5, 9, 17, 37, 41, 73, 137, 149, 153, 257, 261, 277, 293, 337, 405, 521, 529, 549, 577, 593, 641, 661, 673, 677, 1025, 1033, 1061, 1093, 1097, 1109, 1153, 1193, 1289, 1297, 1301, 1321, 1361, 2053, 2069, 2081, 2089, 2097, 2113, 2129, 2209, 2213, 2225, 2309, 2341, 2377, 2389, 2593, 2633, 2689, 2693, 2729, 2825, 4129, 4133, 4177, 4229

Offset: 1

Author

Antti Karttunen, Mar 14 2019

Keywords

• nonn

Comments

Odd numbers n for which 2*A318458(n) = A318468(n). If there are no common terms with A324719, then there are no odd perfect numbers.

This is not a subsequence of A191218, because terms 1, 9, 529, 2209, 10609, 77841, 83521, 263169, 279841, 330625, 528529, ... are not present in A191218.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to binary expansion of n
• Index entries for sequences where any odd perfect numbers must occur
• Index entries for sequences related to sigma(n)

Crossrefs

Subsequence of A324639.

Cf. A004198, A191218, A318458, A318468, A324647, A324719, A324727.

Programs

Mathematica

Select[Range[1, 10^4, 2], Block[{s = DivisorSigma[1, #]}, BitAnd[2*#, s] == 2* BitAnd[#, s-#]] &] (* Paolo Xausa, Mar 11 2024 *)

PARI

for(n=1,oo,if((n%2) && (bitand(2*n,sigma(n)) == 2*bitand(n,sigma(n)-n)),print1(n, ", ")));