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

1,2

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).

Links

Table of n, a(n) for n=1..64.

Example

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

Mathematica

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

Prog

(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

Crossrefs

Intersection of A056911 and A073485.

Cf. A065091, A294472.

Sequence in context: A368100 A302568 A359260 * A340077 A179458 A062086

Adjacent sequences: A294671 A294672 A294673 * A294675 A294676 A294677

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, Nov 06 2017

Extensions

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

Status

approved