OFFSET
1,1
COMMENTS
Previous name was: Let p^b(n,p) be the largest power of the prime p that divides n. The integer n is included if the list of p^b(n,p)'s, where each p is a distinct prime divisor of n, arranged by size of each p^b(n,p) is not in the same order as the list of p^b(n,p)'s arranged by size of each prime p.
This sequence contains no squarefree integers.
90 is the smallest integer in this sequence but not in sequence A126855.
The number of terms < 10^n: 0, 12, 151, 1575, 16154, 161630, 1617052, ..., . - Robert G. Wilson v, Aug 31 2008
If k is in the sequence, then all powers of k are in the sequence. - Mike Jones, Jun 16 2022
If k is in the sequence then k*A020639(k)^m is in the sequence for m >= 0. - David A. Corneth, Jun 16 2022
Conjecture: There are infinitely many terms k such that k+1 is also a term. - Mike Jones, Jun 18 2022
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10000
EXAMPLE
The prime factorization of 90 is, when arranged by size of the distinct primes, 2^1 * 3^2 * 5^1. Since 3^2 is > 5^1, even though 5 > 3, 90 is in the sequence.
MATHEMATICA
fQ[n_] := Block[{f = First@# ^ Last@# & /@ FactorInteger@n}, f != Sort@f]; Select[ Range@ 407, fQ@# &] (* Robert G. Wilson v, Aug 31 2008 *)
PROG
(PARI) is(n) = { my(f = factor(n)); for(i = 1, #f~-1, if(f[i, 1]^f[i, 2] > f[i+1, 1]^f[i+1, 2], return(1) ) ); 0 } \\ David A. Corneth, Jun 16 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Leroy Quet, Jul 18 2008
EXTENSIONS
More terms from Robert G. Wilson v, Aug 31 2008
Simpler name from Mike Jones, Jun 15 2022
STATUS
approved