cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A364498 Odd numbers k such that k divides A243071(k).

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%I A364498 #16 Jul 27 2023 21:13:41
%S A364498 1,3,43,1177,3503,49477,169413,428015,4394113,33228911
%N A364498 Odd numbers k such that k divides A243071(k).
%C A364498 Primes p present are those that occur as factors of (2^A000720(p))-1: 3, 43, 49477, 4394113, 33228911, ...
%H A364498 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%e A364498 1177 = 11 * 107, with A243071(1177) = 536870895 = 3*5*11*47*107*647, therefore 1177 is present. Note that 536870895 = 11111111111111111111111101111 in binary, with four 1-bits at the least significant end, followed by 0, and then 24 more 1-bits at the most significant end, so A163511(536870895) = A000040(1+4) * A000040(4+24) = 11 * 107.
%o A364498 (PARI)
%o A364498 A054429(n) = ((3<<#binary(n\2))-n-1); \\ From A054429
%o A364498 A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
%o A364498 A243071(n) = if(n<=2, n-1, A054429(A156552(n)));
%o A364498 isA364498(n) = ((n%2)&&!(A243071(n)%n));
%Y A364498 Odd terms in A364497.
%Y A364498 Cf. A000720, A163511, A243071, A364256.
%K A364498 nonn,more
%O A364498 1,2
%A A364498 _Antti Karttunen_, Jul 27 2023
%E A364498 a(10) from _Chai Wah Wu_, Jul 27 2023