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