A324643 Numbers k such that bitand(2k,sigma(k))/2 = k = bitand(k,sigma(k)-k), where bitand is bitwise-AND, A004198.

6, 20, 28, 36, 88, 100, 104, 264, 272, 304, 368, 392, 464, 496, 550, 784, 1032, 1040, 1044, 1056, 1068, 1104, 1120, 1184, 1232, 1312, 1376, 1504, 1696, 1888, 1952, 2140, 3222, 4100, 4128, 4160, 4288, 4512, 4544, 4624, 4640, 4672, 5056, 5312, 5696, 6208, 6328, 6464, 6592, 6808, 6848, 6976, 7232, 7304, 8128, 8288, 8968, 9256, 10184

Offset

1,1

Comments

Numbers k for which k = A318458(k)/2 = A318468(k).

Intersection of A324649 and A324652.

It is conjectured that there are no odd terms in this sequence, which is equivalent to the conjecture that there are no odd perfect numbers.

Question: Where do the densest clusters of terms occur? See also the scatter plot. - Antti Karttunen, Mar 12 2024

Links

Antti Karttunen, Table of n, a(n) for n = 1..17020

Michael De Vlieger, Log log scatterplot of a(n), n = 1..17020, labeling cusps in the plot.

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)

Mathematica

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

Prog

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

Crossrefs

Cf. A004198, A318458, A318468.

Intersection of A324649 and A324652.

Subsequence of A324639.

Sequence in context: A316291 A090502 A324649 * A119425 A342669 A006039

Adjacent sequences: A324640 A324641 A324642 * A324644 A324645 A324646

Keyword

nonn,look

Author

Antti Karttunen, Mar 14 2019

Status

approved