A053159 - OEIS

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A053159

Numbers n such that n+cototient(n) is a power of 2.

1, 3, 7, 10, 20, 31, 40, 80, 127, 160, 320, 322, 640, 644, 1280, 1288, 2560, 2576, 5120, 5152, 8191, 10240, 10304, 20480, 20608, 40960, 41216, 81920, 82432, 131071, 163840, 164864, 327680, 329728, 333634, 524287, 655360, 659456, 667268, 1310720, 1318912

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

See especially A053579 and also A053576, A053577.

LINKS

Donovan Johnson, Table of n, a(n) for n = 1..100

FORMULA

a(n)+A051953(n) = 2*a(n)-A000010(n) = 2^w for some w.

EXAMPLE

Mersenne primes are a proper subset of this sequence: A(M)=2M-M+1=M+1=2^p

PROG