A102308 If n = product{primes p(k)|n} p(k)^b(n,p(k)), where p(k) is the k-th 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 non-prime-powers 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.

12, 24, 36, 40, 45, 48, 56, 63, 72, 80, 96, 108, 112, 135, 144, 160, 175, 176, 180, 189, 192, 200, 208, 216, 224, 225, 252, 275, 288, 297, 320, 324, 325, 351, 352, 360, 384, 392, 400, 405, 416, 425, 432, 441, 448, 459, 475, 504, 513, 539, 540, 544, 567, 575

Offset

1,1

Links

Table of n, a(n) for n=1..54.

Example

252 is factored as 2^2 * 3^2 * 7^1. Since 2^2 > 3 and 3^2 > 7, then 252 is in the sequence. On the other hand, 60 is factored as 2^2 * 3^1 * 5^1. Even though 2^2 > 3, 3^1 is not > 5. So 60 is not in the sequence.

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. A057715, A143907.

Sequence in context: A195556 A083547 A009185 * A354583 A103291 A103292

Adjacent sequences: A102305 A102306 A102307 * A102309 A102310 A102311

Keyword

nonn

Author

Leroy Quet, Sep 04 2008

Extensions

Extended by Ray Chandler, Nov 06 2008

Status

approved