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A094348 Numbers n such that, for some numbers (j,k), j<=k, n is the smallest positive multiple of j (or more) of the first k positive integers. 16
1, 2, 4, 6, 12, 24, 36, 48, 60, 72, 120, 180, 240, 360, 420, 720, 840, 1260, 1680, 2520, 5040, 7560, 10080, 15120, 20160, 25200, 27720, 30240, 45360, 50400, 55440, 83160, 110880, 166320, 221760, 277200, 332640, 360360, 498960, 554400, 665280, 720720 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Includes all highly composite numbers (A002182) and least common multiples of 1 through n (A003418). It would be interesting to know: 1) whether or not all deeply composite numbers (A095848, which includes all members of A003418) also belong to this sequence; 2) if 72 is the only member of this sequence not also belonging to A002182 or A095848.

465585120 is the first member of A095848 that is not a member of this sequence. The first members that belong to neither A002182 nor A095848 are 72, 30240, 64864800 and 1470268800. - David Wasserman, Jun 28 2007

This sequence is also A096179 with duplicates deleted and sorted. Let F(n) be the number of the row of A096179 which has the first occurence of a(n) and M(n) = max{F(i),i <= n}. Then the following table indicates this connection.

  n |1,2,3,4, 5, 6, 7, 8, 9,10, 11, 12, 13, 14, 15, 16, 17,  18,  19,  20, 21

a(n)|1,2,4,6,12,24,36,48,60,72,120,180,240,360,420,720,840,1260,1680,2520,5040

F(n)|1,2,4,3, 4, 8,18,16, 5, 9,  8, 18, 16,  9,  7, 16, 15,  21,  16,   9, 16

M(n)|1,2,4,4, 4, 8,18,18,18,18, 18, 18, 18, 18, 18, 18, 18,  21,  21,  21, 21

- Peter Luschny, Dec 29 2010

LINKS

Table of n, a(n) for n=1..42.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 844.

J. Britton, Perfect Number Analyzer

Wikipedia, Table of divisors.

Peter Luschny, More terms, OEIS wiki.

EXAMPLE

72 is a multiple of seven of the first nine positive integers (namely, 1, 2, 3, 4, 6, 8 and 9). It is the smallest positive integer for which this is true.

PROG

(PARI) \\ Computes the first 50 terms of A094348

A094348() = {local(n, i, R, A, len, count, change, high, lim);

lim = 7208000; R = vector(500); A = vector(50); A[1]=1;

A[2]=2; A[3]=4; A[4]=6; A[5]=12; count=5; high=0; n=12;

while(n < lim, d=divisors(n); len=length(d); change=0;

for(i=1, min(len, high), if(R[i]>d[i], R[i]=d[i]; change=1));

if(len>high, for(i=high+1, len, R[i]=d[i]); high=len);

if(change, count++; A[count] = n); n += 12; );

write("A094348.txt", vector(count, i, A[i])); }

\\ Peter Luschny, Dec 29 2010

CROSSREFS

Cf. A096179, A003418, A002182, A002201, A072938, A106037, A002110.

Sequence in context: A141420 A141551 A181804 * A242298 A189686 A002182

Adjacent sequences:  A094345 A094346 A094347 * A094349 A094350 A094351

KEYWORD

nonn

AUTHOR

Matthew Vandermast, Jun 18 2004, Oct 12 2008

EXTENSIONS

More terms from David Wasserman, Jun 28 2007

Title edited by Matthew Vandermast, Nov 20 2010

STATUS

approved

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Last modified May 29 22:45 EDT 2017. Contains 287257 sequences.