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Semiprimes k such that k is divisible by its index in the sequence of semiprimes.
2

%I #56 Oct 29 2022 04:42:53

%S 4,6,9,21,33,129,159,3066835,3067195,3067255,3067615,3067745,3068045,

%T 44690978227,44690978647,44690978983,44690979529

%N Semiprimes k such that k is divisible by its index in the sequence of semiprimes.

%C No further terms <= 8040423200947. - _Lucas A. Brown_, Oct 13 2022

%C Conjecture: a(18) > 10^17. - _Martin Ehrenstein_, Oct 28 2022

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/semiprimemods.py">semiprimemods.py</a>

%F a(n) = A001358(A106125(n))

%e The 1st semiprime is 4, which is divisible by 1, so 4 is in the sequence.

%e The 4th semiprime is 10, which is not divisible by 4, so 10 is not in the sequence.

%e The 7th semiprime is 21, which is divisible by 7, so 21 is in the sequence.

%Y Cf. A001358, A106125, A356764.

%K nonn,hard,more

%O 1,1

%A _Lucas A. Brown_, Oct 13 2022