This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A055926 Numbers n such that {largest m such that 1, 2, ..., m divide n} is different from {largest m such that m! divides n}; numbers n which are either odd multiples of 12 or the largest m such that (m-1)! divides n is a composite number > 5. 12
 12, 36, 60, 84, 108, 120, 132, 156, 180, 204, 228, 240, 252, 276, 300, 324, 348, 360, 372, 396, 420, 444, 468, 480, 492, 516, 540, 564, 588, 600, 612, 636, 660, 684, 708, 732, 756, 780, 804, 828, 840, 852, 876, 900, 924, 948, 960, 972, 996, 1020, 1044, 1068 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Contribution from Antti Karttunen, Nov 20 - Dec 06 2013: (Start) This sequence has several interpretations: Numbers n such that A055874(n) differs from A055881(n). [Leroy Quet's original definition of the sequence. Note that A055874(n) >= A055881(n) for all n]. Numbers n such that {largest m such that m! divides n^2} is different from {largest m such that m! divides n}, i.e. numbers n for which A232098(n) > A055881(n). Numbers n which are either 12 times an odd number (A073762) or the largest m such that (m-1)! divides n is a composite number > 5 (A232743). Please see my attached notes for the proof of the equivalence of these interpretations. Additional implications based on that proof: A232099 is a subset of this sequence. A055881(a(n))+1 is always composite. In range n=1..17712, only values 4, 6, 8, 9 and 10 occur. The new definition can be also rephrased by saying that the sequence contains all the natural numbers n whose factorial base representation of (A007623(n)) either ends as '...200' (in which case n is an odd multiple of 12, 12 = '200', 36 = '1200', 60 = '2200', ...) or the number of trailing zeros + 2 in that representation is a composite number greater than or equal to 6 , e.g. 120 = '10000' (in other words, A055881(n) is one of the terms of A072668 after the initial 3). Together these conditions also imply that all the terms are divisible by 12. (End) LINKS Antti Karttunen, Table of n, a(n) for n = 1..17712 Wikipedia, Wilson's theorem (See the section "Composite modulus") EXAMPLE 12 is included because 3! is the highest factorial to divide 12, but 1, 2, 3 and 4 all divide 12. Equally, 12 is included because it is one of the terms of A073762, or equally, because its factorial base representation ends with digits '...200': A007623(12) = 200. 840 (= 3*5*7*8) is included because the highest factorial which divides 840 is 5! (840 = 7*120), but all natural numbers up to 8 divide 840. Equally, 840 is included because it is one of the terms of A232743 as 5+1 = 6 is a composite number larger than 5. Note that A007623(840) = 110000. PROG (Scheme, with Antti Karttunen's IntSeq-library) (define A055926 (MATCHING-POS 1 1 (lambda (n) (not (= (A055874 n) (A055881 n)))))) ;; Antti Karttunen, Nov 18 2013 (define A055926 (MATCHING-POS 1 1 (lambda (n) (cond ((and (integer? (/ n 12)) (odd? (/ n 12)))) ((A055881 n) => (lambda (k) (and (> k 4) (not (prime? (+ k 1)))))))))) ;; Antti Karttunen, Dec 01 2013 CROSSREFS Union of A073762 and A232743. Equivalently, setwise difference of A232742 and A017593. Subset: A232099. Cf. A055874, A055881, A072668, A232098, A232100, A232741, A232744, A232745. Sequence in context: A298942 A322411 A063298 * A073762 A211609 A043140 Adjacent sequences:  A055923 A055924 A055925 * A055927 A055928 A055929 KEYWORD easy,nonn AUTHOR Leroy Quet, Jul 16 2000 EXTENSIONS More terms from Antti Karttunen, Dec 01 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 21 14:33 EDT 2019. Contains 328301 sequences. (Running on oeis4.)