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.

A080361 a(n) is the difference between the largest and the smallest positive integers x such that the number of unitary-prime-divisors of x! equals n. Same as the difference between the largest and the smallest positive integers x such that the number of primes in (x/2,x] equals n.

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%I A080361 #9 Feb 16 2025 08:32:48
%S A080361 8,13,15,21,15,15,13,9,25,27,5,23,39,37,27,21,7,45,37,39,39,1,21,17,
%T A080361 11,35,27,53,35,17,19,27,29,9,11,11,5,21,43,27,11,69,61,63,15,5,1,5,
%U A080361 33,29,27,5,5,17,57,43,47,17,25,51,47,11,3,25,27,23,77,57,35,19,29,37,27,23,9
%N A080361 a(n) is the difference between the largest and the smallest positive integers x such that the number of unitary-prime-divisors of x! equals n. Same as the difference between the largest and the smallest positive integers x such that the number of primes in (x/2,x] equals n.
%H A080361 J. Sondow, <a href="https://mathworld.wolfram.com/RamanujanPrime.html">Ramanujan Prime in MathWorld</a> [From _Jonathan Sondow_, Aug 10 2008]
%F A080361 a(n)=Max{x; Pi[x]-Pi[x/2]=n}-Min{x; Pi[x]-Pi[x/2]=n}=A080360[n]-A080359[n].
%Y A080361 Cf. A056171, A056169, A000720, A000142, A080359, A080360.
%Y A080361 Cf. A104272 Ramanujan primes. [From _Jonathan Sondow_, Aug 10 2008]
%K A080361 nonn
%O A080361 1,1
%A A080361 _Labos Elemer_, Feb 21 2003
%E A080361 Definition corrected by _Jonathan Sondow_, Aug 10 2008
%E A080361 Typo in formula corrected by _Daniel Forgues_, Aug 06 2009