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.
%I A340624 #24 Apr 26 2021 08:59:44 %S A340624 16,32,64,128,256,512,768,1024,1536,2048,2304,3072,4096,4608,6144, %T A340624 8192,9216,12288,16384,18432,24576,32768,36864,49152,65536,73728, %U A340624 98304,110592,131072,147456,165888,196608,221184,248832,262144,294912,331776,373248,393216,442368 %N A340624 Numbers k such that A340388(k) > A018782(k). %C A340624 Numbers k such that A340388(k) is not the smallest number whose prime factors are all congruent to 1 modulo 4 and with exactly k divisors. %C A340624 Despite being an analog of A072066, this sequence seems to be considerably sparser than A072066. What's the reason for that? %C A340624 All powers of 2 that are greater than or equal to 16 are here. All numbers of the form 3 * 2^e with e >= 8 are here. %C A340624 All powers of 3 that are greater than or equal to 3^15 = 14348907 are here. For example, we have A340388(3^15) = (5 * 13 * 17 * 29 * ... * 113 * 137)^2, while a(3^15) <= (5^4 * 13 * 17 * 29 * .. * 113)^2, so 3^15 is a term. Apparently 3^15 is the smallest odd term in this sequence. %C A340624 Similarly, let q be a prime, then all powers of q that are greater than or equal to q^(N+1) are here, where N is the number of primes congruent to 1 modulo 4 below 5^q. It seems that q^(N+1) is the smallest q-rough term in this sequence. %e A340624 16 is a term since A340388(16) = 5 * 13 * 17 * 29 > A018782(16) = 5^3 * 13 * 17. %o A340624 (PARI) isA340624(n) = (A340388(n) > A018782(n)) \\ See A018782 and A340388 for their programs %Y A340624 Cf. A018782, A340388, A072066. %K A340624 nonn,hard %O A340624 1,1 %A A340624 _Jianing Song_, Apr 25 2021