A202274 Positive integers m in increasing order determined by these rules: a(1) = 1, for n>=1, if m is in the sequence then also are numbers h such that sigma(h) = 4m-1.

1, 2, 4, 8, 16, 25, 32, 64, 128, 256, 512, 1024, 2048, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296

Offset

1,2

Comments

If 31 is only number h of form 2^k-1 for any k>=1 such that sigma(x) = h has solution for more than one value of x then a(n) is union number 25 with A000079 (powers of 2).

Links

Table of n, a(n) for n=1..36.

Example

 m=1, 4m-1=3, sigma(h)=3 for h=2; number 2 is in sequence.
m=2, 4m-1=7, sigma(h)=7 for h=4; number 4 is in sequence.
m=4, 4m-1=15, sigma(h)=15 for h=8; number 8 is in sequence.
m=8, 4m-1=31, sigma(h)=31 for h=16 and 25; numbers 16 and 25 are in sequence.

Crossrefs

Cf. A000203, A002191, A202273.

Sequence in context: A305183 A360642 A112992 * A070789 A302588 A348656

Adjacent sequences: A202271 A202272 A202273 * A202275 A202276 A202277

Keyword

nonn

Author

Jaroslav Krizek, Dec 25 2011

Status

approved