A294674 Numbers that are the product of any number of consecutive odd primes.

1, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31, 35, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 77, 79, 83, 89, 97, 101, 103, 105, 107, 109, 113, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 221, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 06 2017

Keywords

• nonn
• easy

Comments

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).

Examples

			105 is in this sequence because 105 = 3*5*7 = A065091(1)*A065091(2)*A065091(3), where A065091() are odd primes.
		

Crossrefs

Intersection of A056911 and A073485.

Cf. A065091, A294472.

Programs

Mathematica

{1}~Join~Select[Range[3, 275, 2], And[SquareFreeQ@ #, MemberQ[{{}, {1}}, Union@ Differences@ PrimePi@ FactorInteger[#][[All, 1]]]] &] (* Michael De Vlieger, Nov 15 2017 *)

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

Extensions

a(57) corrected by Rémy Sigrist, Nov 18 2017