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%I #34 Feb 03 2018 12:18:20
%S 1,3,5,7,11,13,15,17,19,23,29,31,35,37,41,43,47,53,59,61,67,71,73,77,
%T 79,83,89,97,101,103,105,107,109,113,127,131,137,139,143,149,151,157,
%U 163,167,173,179,181,191,193,197,199,211,221,223,227,229,233,239,241,251,257,263,269,271
%N Numbers that are the product of any number of consecutive odd primes.
%C If a(n) is an odd squarefree number with no gaps in its prime >= A065091(1) factors, b(n) is an odd squarefree number with no gaps in its prime >= A065091(2) factors, and c(n) is an odd squarefree number with no gaps in its prime >= A065091(3) factors, ..., then a(n) >= b(n) >= c(n) >= ... >= A056911(n).
%e 105 is in this sequence because 105 = 3*5*7 = A065091(1)*A065091(2)*A065091(3), where A065091() are odd primes.
%t {1}~Join~Select[Range[3, 275, 2], And[SquareFreeQ@ #, MemberQ[{{}, {1}}, Union@ Differences@ PrimePi@ FactorInteger[#][[All, 1]]]] &] (* _Michael De Vlieger_, Nov 15 2017 *)
%o (PARI) isok(n) = {if ((n % 2) && issquarefree(n), f = factor(n); v = vector(#f~, k, primepi(f[k,1])); for (k=2, #v, if (v[k] - v[k-1] != 1, return (0))); return (1);); return (0);} \\ _Michel Marcus_, Nov 08 2017
%Y Intersection of A056911 and A073485.
%Y Cf. A065091, A294472.
%K nonn,easy
%O 1,2
%A _Juri-Stepan Gerasimov_, Nov 06 2017
%E a(57) corrected by _Rémy Sigrist_, Nov 18 2017
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