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A232743 Numbers n for which the largest m such that (m-1)! divides n is a composite number > 5. 7

%I #11 Dec 05 2013 08:35:49

%S 120,240,360,480,600,840,960,1080,1200,1320,1560,1680,1800,1920,2040,

%T 2280,2400,2520,2640,2760,3000,3120,3240,3360,3480,3720,3840,3960,

%U 4080,4200,4440,4560,4680,4800,4920,5040,5160,5280,5400,5520,5640,5880,6000,6120,6240

%N Numbers n for which the largest m such that (m-1)! divides n is a composite number > 5.

%C Numbers n for which A055881(n)>4 and is one of the terms of A072668.

%C Numbers n for which two plus the number of the trailing zeros in their factorial base representation A007623(n) is a composite number larger than 5.

%C All terms are multiples of 120. Specifically, these are all those terms of A232742 which are divisible by 120 (or equally: 24).

%C Please see also the comments in A055926, whose subset this sequence is.

%H Antti Karttunen, <a href="/A232743/b232743.txt">Table of n, a(n) for n = 1..25920</a>

%e 120 is included because A055881(120)=5 and 5+1 is a composite number larger than 5. Note that A007623(120) = '10000', with four trailing zeros.

%e 720 is the first missing multiple of 120, as A055881(720)=6 and 7 is a prime, not composite, so 720 is not included in this sequence. Note that A007623(720) = '100000', with five trailing zeros, and 5+2 is not a composite.

%e 120960 (= 3*8!) is included because A055881(120960)=8 and 9 is a composite number larger than 5. Note that A007623(120960) = '30000000', with seven trailing zeros.

%o (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (define A232743 (MATCHING-POS 1 1 (lambda (n) (cond ((A055881 n) => (lambda (k) (and (> k 4) (not (prime? (+ k 1))))))))))

%Y Subset of both A232742 and A055926.

%Y Cf. also A007623, A055881, A230403, A232744-A232745.

%K nonn

%O 1,1

%A _Antti Karttunen_, Dec 01 2013

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Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)