

A294674


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


1



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
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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[k1] != 1, return (0))); return (1); ); return (0); } \\ Michel Marcus, Nov 08 2017


CROSSREFS

Intersection of A056911 and A073485.
Cf. A065091, A294472.
Sequence in context: A272872 A103796 A302568 * A340077 A179458 A062086
Adjacent sequences: A294671 A294672 A294673 * A294675 A294676 A294677


KEYWORD

nonn,easy


AUTHOR

JuriStepan Gerasimov, Nov 06 2017


EXTENSIONS

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


STATUS

approved



