A332216 Fixed points of A332221: Numbers k such that A156552(sigma(k)) is equal to k.

2, 3, 5, 7, 11, 19, 23, 31, 47, 55, 79, 87, 127, 191, 383, 1279, 5119, 6143, 8191, 20479, 81919, 131071, 524287, 786431, 1310719, 2147483647

Offset

1,1

Comments

Equally, numbers k such that sigma(k) is equal to A005940(1+k).

The primes in this sequence are obtained by subtracting 1 from those terms of A029747 that are one more than a prime.

Questions: Are there other composite terms than 55 and 87? Are there other even terms than 2? (All such even terms should also occur in A332218).

Links

Table of n, a(n) for n=1..26.

Index entries for sequences related to binary expansion of n

Index entries for sequences related to sigma(n)

Mathematica

Select[Range[10^5], DivisorSigma[1, #] == Block[{p = Partition[Split[Join[IntegerDigits[#, 2], {2}]], 2], q}, Times @@ Flatten[Table[q = Take[p, -i]; Prime[Count[Flatten[q], 0] + 1]^q[[1, 1]], {i, Length[p]}]]] &] (* Michael De Vlieger, Feb 12 2020, after Robert G. Wilson v at A005940 *)

Crossrefs

Cf. A000203, A005940, A029747, A156552, A332217, A332218, A332221.

Subsequences: A000668, A007505, A050522.

Sequence in context: A214837 A079346 A228062 * A059878 A105017 A214197

Adjacent sequences: A332213 A332214 A332215 * A332217 A332218 A332219

Keyword

nonn,more

Author

Antti Karttunen, Feb 10 2020

Status

approved