A319354 -id:A319354 - cp's OEIS frontend

A067131 Number of elements in the largest set of divisors of n which are in arithmetic progression.

1, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 4, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 4, 2, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 6, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 2, 4, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 3, 2

Offset: 1

Amarnath Murthy, Jan 09 2002

			a(12) = 4 as the divisors of 12 are {1,2,3,4,6,12} and the maximal subset in arithmetic progression is {1,2,3,4}. a(15) = 3; the maximal set is {1,3,5}.

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A067132, A091009, A160752, A319354.

lap[s_] := Module[{}, l=Length[s]; If[l<2, Return[l]]; val=2; For[i=1, ival, val=k]]]; val]; lap/@Divisors/@Range[1, 200]

A067131(n) = { my(d=divisors(n),m=1); for(i=1,(#d-1), for(j=(i+1),#d,my(c=1,k=d[j],s=(d[j]-d[i])); while(!(n%k), k+=s; c++); m = max(m,c))); (m); }; \\ Antti Karttunen, Sep 21 2018

a(n) = A061395(A319354(n)). - Antti Karttunen, Sep 21 2018

Edited by Dean Hickerson, Jan 15 2002

A160752 a(n) is the number of sets of (distinct, not necessarily consecutive) positive divisors of n where each set has all of its elements in arithmetic progression, and where each set contains exactly A067131(n) elements.

Original entry on oeis.org

1, 1, 1, 3, 1, 1, 1, 6, 3, 6, 1, 1, 1, 6, 1, 10, 1, 2, 1, 15, 6, 6, 1, 2, 3, 6, 6, 1, 1, 4, 1, 15, 6, 6, 6, 2, 1, 6, 6, 1, 1, 2, 1, 15, 3, 6, 1, 3, 3, 15, 6, 15, 1, 3, 6, 2, 6, 6, 1, 1, 1, 6, 15, 21, 6, 3, 1, 15, 6, 28, 1, 4, 1, 6, 2, 15, 6, 2, 1, 2, 10, 6, 1, 2, 6, 6, 6, 28, 1, 10, 1, 15, 6, 6, 6, 4, 1, 15

Offset: 1

Leroy Quet, May 25 2009

nonn

If A067131(n) = 2, then a(n) = d(n)*(d(n)-1)/2, where d(n) is the number of divisors of n.

a(p) = 1 for all primes p.

			The divisors of 18 are 1,2,3,6,9,18. There are 2 sets of these divisors, (1,2,3) and (3,6,9), that have their terms in arithmetic progression and that each have the maximal number (3) of such divisors of 18. So a(18) = 2.

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A067131, A319354.

A160752(n) = if(1==n,n,my(d=divisors(n),m=1,counts=vector(#d)); for(i=1,(#d-1), for(j=(i+1),#d,my(c=1,k=d[j],s=(d[j]-d[i])); while(!(n%k), k+=s; c++); counts[c]++; m = max(m,c))); (counts[m])); \\ Antti Karttunen, Sep 21 2018

a(n) = A071178(A319354(n)). - Antti Karttunen, Sep 21 2018

Extended by Ray Chandler, Jun 15 2009

A319355 Filter sequence constructed from the lengths of arithmetic progressions occurring among the divisors of n.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 5, 3, 5, 2, 6, 2, 5, 4, 7, 2, 8, 2, 9, 5, 5, 2, 10, 3, 5, 5, 11, 2, 12, 2, 9, 5, 5, 5, 13, 2, 5, 5, 14, 2, 15, 2, 9, 16, 5, 2, 17, 3, 9, 5, 9, 2, 18, 5, 15, 5, 5, 2, 19, 2, 5, 9, 20, 5, 18, 2, 9, 5, 21, 2, 22, 2, 5, 8, 9, 5, 15, 2, 23, 7, 5, 2, 24, 5, 5, 5, 21, 2, 25, 4, 9, 5, 5, 5, 26, 2, 9, 9, 27, 2, 15, 2, 21, 28

Offset: 1

Antti Karttunen, Sep 21 2018

nonn

Restricted growth sequence transform of A319354.
For all i, j:
  a(i) = a(j) => A067131(i) = A067131(j).
  a(i) = a(j) => A160752(i) = A160752(j).
  a(i) = a(j) => A091009(i) = A091009(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A319354.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A319354(n) = if(1==n,2,my(d=divisors(n),m=1); for(i=1,(#d-1), for(j=(i+1),#d,my(c=1,k=d[j],s=(d[j]-d[i])); while(!(n%k), k+=s; c++); m *= prime(c))); (m));
v319355 = rgs_transform(vector(up_to,n,A319354(n)));
A319355(n) = v319355[n];

cp's OEIS Frontend

A067131 Number of elements in the largest set of divisors of n which are in arithmetic progression.

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A160752 a(n) is the number of sets of (distinct, not necessarily consecutive) positive divisors of n where each set has all of its elements in arithmetic progression, and where each set contains exactly A067131(n) elements.

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Author

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Examples

Links

Crossrefs

Programs

PARI

Formula

Extensions

A319355 Filter sequence constructed from the lengths of arithmetic progressions occurring among the divisors of n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI