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 A378659 #17 Dec 06 2024 10:40:48 %S A378659 1,3,4,7,8,9,16,27,32,64,128,243,256,512,1024,2048,4096,8192,16384, %T A378659 32768,65536,131072,262144,524288,1048576,2097152,4194304,8388608, %U A378659 16777216,33554432,67108864 %N A378659 Positions of records for ratio A003961(n)/sigma(n), where A003961 is fully multiplicative with a(p) = nextprime(p) and sigma is the sum of the divisors function. %H A378659 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a> %H A378659 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a> %e A378659 Term k A003961(k)/A000203(k) ratio %e A378659 1 1/1 = 1 %e A378659 3 5/4 = 1.25 %e A378659 4 9/7 = 1.2857143 %e A378659 7 11/8 = 1.375 %e A378659 8 27/15 = 1.8 %e A378659 9 25/13 = 1.9230769 %e A378659 16 81/31 = 2.6129032 %e A378659 27 125/40 = 3.125 %e A378659 32 243/63 = 3.8571429 %e A378659 64 729/127 = 5.7401575 %e A378659 128 2187/255 = 8.5764706 %e A378659 243 3125/364 = 8.5851648 %e A378659 256 6561/511 = 12.839530 %e A378659 ... %e A378659 33554432 847288609443/67108863 = 12625.584 %e A378659 67108864 2541865828329/134217727 = 18938.376 %Y A378659 Cf. A000203, A003961. %Y A378659 Cf. A001359 (apparently gives the positions of successive minima of the ratio, for n > 2). %Y A378659 Cf. also A341529, A349627, A349628, A354827, A354828. %K A378659 nonn %O A378659 1,2 %A A378659 _Antti Karttunen_, Dec 06 2024