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A354536
Numbers k such that 2*k is in A354525.
3
1, 3, 7, 31, 127, 511, 8191, 131071, 524287, 2147483647, 2305843009213693951, 147573952589676412927, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727, 174224571863520493293247799005065324265471
OFFSET
1,2
COMMENTS
Numbers k such that for every prime factor p of k we have gpf(2*k+p) = p, gpf = A006530.
Numbers k such that for every prime factor p of k, 2*k+p is p-smooth.
FORMULA
a(n) = 2^A354531(n) - 1 = A354533(n)/2.
EXAMPLE
See A354532.
PROG
(PARI) lista(nn, {lim=256}, {lim_p=1<<32}) = for(n=1, nn, if(isA354531(n, lim, lim_p), print1(2^n-1, ", "))) \\ See A354531 for the function isA354531
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Jianing Song, Aug 17 2022
STATUS
approved