

A143907


If n = product{primes p(k)n} p(k)^b(n,p(k)), where p(k) is the kth prime that divides n (when these primes are listed from smallest to largest) and each b(n,p(k)) is a positive integer, then the sequence contains the nonprimepowers n such that p(k)^b(n,p(k)) < p(k+1) for all k, 1<=k<= 1 + number of distinct prime divisors of n.


1



6, 10, 14, 15, 18, 20, 21, 22, 26, 28, 30, 33, 34, 35, 38, 39, 42, 44, 46, 50, 51, 52, 54, 55, 57, 58, 62, 65, 66, 68, 69, 70, 74, 75, 76, 77, 78, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 98, 99, 100, 102, 104, 105, 106, 110, 111, 114, 115, 116, 117, 118, 119, 122, 123, 124
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..65.


EXAMPLE

2900 is factored as 2^2 * 5^2 * 29^1. Since 2^2 < 5 and 5^2 < 29, then 2900 is in the sequence. On the other hand, 60 is factored as 2^2 * 3^1 * 5^1. Even though 3^1 < 5, 2^2 is not < 3. So 60 is not in the sequence.


MATHEMATICA

okQ[n_] := With[{f = FactorInteger[n]}, If[Length[f] == 1, Return[False]]; For[i = 1, i < Length[f], i++, If[f[[i, 1]]^f[[i, 2]] >= f[[i+1, 1]], Return[False]]]; True]; Select[Range[200], okQ] (* JeanFrançois Alcover, May 16 2017, adapted from PARI *)


PROG

(PARI) isok(n) = {my(f = factor(n)); if (#f~ == 1, return (0)); for (i=1, #f~  1, if (f[i, 1]^f[i, 2] >= f[i+1, 1], return (0)); ); return (1); } \\ Michel Marcus, Jan 19 2014


CROSSREFS

Cf. A057714, A102308.
Sequence in context: A085232 A085234 A057714 * A132982 A300080 A069169
Adjacent sequences: A143904 A143905 A143906 * A143908 A143909 A143910


KEYWORD

nonn


AUTHOR

Leroy Quet, Sep 04 2008


EXTENSIONS

Extended by Ray Chandler, Nov 06 2008


STATUS

approved



