A383836 Integers k such that d*2^k + k/d is prime for some divisor d of k.
1, 3, 5, 6, 9, 10, 15, 21, 22, 28, 39, 66, 75, 81, 89, 105, 108, 111, 141, 165, 166, 190, 196, 317, 340, 357, 459, 462, 483, 525, 564, 568, 573, 701, 735, 737, 792, 869, 1185, 1311, 1480, 1647, 1794, 1881, 2145, 2405, 2508, 2766, 3081, 3201, 3225, 3243, 4260, 4713, 5369, 5795, 5985
Offset: 1
Keywords
Examples
6 is a term because 2*2^6 + 6/2 = 131 is prime for divisor d = 2 of k = 6.
Programs
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Magma
[k: k in [1..1000] | not #[d: d in Divisors(k) | IsPrime(d*2^k+(k div d))] eq 0];
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Mathematica
Select[Range[4300],Sum[Boole[PrimeQ[d*2^#+#/d]],{d,Divisors[#]}]>0 &] (* Stefano Spezia, May 16 2025 *) -
PARI
is(n, f=factor(n))=fordiv(n>>valuation(n,2),d, if(isprime(n/d*2^n+d), return(1))); 0 \\ Charles R Greathouse IV, May 17 2025
Extensions
a(41) corrected by Sean A. Irvine, May 21 2025