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.

A088075 Smallest number sandwiched between two numbers having exactly n prime divisors.

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%I A088075 #21 Sep 27 2023 03:59:55
%S A088075 3,11,131,1429,77141,1456729,117048931,10326137821,1110819807371,
%T A088075 140734085123059,11639258217451019
%N A088075 Smallest number sandwiched between two numbers having exactly n prime divisors.
%C A088075 a(n)=m is the smallest number sandwiched between m-1 and m+1 such that both m+1 and m-1 have n distinct prime-factors. No restrictions are imposed for {m-1,m+1} flanker numbers.
%D A088075 Jean-Marie De Koninck, "Those Fascinating Numbers", American Mathematical Society, 2009, entry 1428. (This gives the lower of the two numbers.)
%F A088075 a(n) = Min{A001221(x-1) = A001221(x+1) = n} x.
%e A088075 n = 3: a(3) = 131, 130 = 2*5*13 and 132 = 2^2*3*11 both have three prime divisors.
%e A088075 n = 6: a(6) = 1456729 = 103*14143 is between 1456728 = 8*3*7*13*23*29 and 1456730 = 2*5*11*17*19*41.
%o A088075 (PARI) isok(k, n) = (omega(k-1)==n) && (omega(k+1)==n);
%o A088075 a(n) = my(k=2); while (!isok(k, n), k++); k; \\ _Michel Marcus_, Sep 03 2023
%Y A088075 Cf. A088076, A088077, A001221.
%K A088075 nonn,more
%O A088075 1,1
%A A088075 _Amarnath Murthy_, Sep 22 2003
%E A088075 Edited by _Labos Elemer_, Sep 30 2003
%E A088075 More terms from _Ray Chandler_, Oct 07 2003
%E A088075 a(8)-a(9) from _Donovan Johnson_, Jun 19 2008
%E A088075 a(10)-a(11) from _Donovan Johnson_, Feb 18 2009