A392668 Numbers m such that sigma(m) = 2*m - omega(m), where omega(m) is the number of distinct prime divisors of m.

2, 4, 8, 10, 16, 32, 64, 128, 136, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 32896, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 815634435, 1073741824, 2147483648, 2147516416

Offset

1,1

Comments

If (2^k+1) is prime and k > 1, then 2^(k-1)*(2^k+1) is in this sequence. All even powers of 2 are in this sequence.

22660587056580139737907204 and 164399910729457037686170602275463956083792004 are also terms.

Links

Alexander Violette, Table of n, a(n) for n = 1..41

Prog

(PARI) for(n=1, 10^5, if(sigma(n)==2*n-omega(n), print(n)))

Crossrefs

Cf. A000203, A001221, A063785.

Sequence in context: A097214 A045579 A177050 * A276772 A173063 A066363

Adjacent sequences: A392665 A392666 A392667 * A392669 A392670 A392671

Keyword

nonn

Author

Alexander Violette, Jan 19 2026

Status

approved