cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A095164 Index of the first occurrence of n in A095163.

Original entry on oeis.org

1, 2, 3, 8, 5, 18, 7, 32, 27, 50, 11, 84, 13, 98, 75, 128, 17, 162, 19, 200, 147, 242, 23, 312, 125, 338, 243, 392, 29, 510, 31, 512, 363, 578, 245, 684, 37, 722, 507, 920, 41, 882, 43, 968, 765, 1058, 47, 1392, 343, 1250, 867, 1352, 53, 1458, 605, 1624, 1083
Offset: 1

Views

Author

Amarnath Murthy, Jun 01 2004

Keywords

Comments

Is this the same as A075384? - R. J. Mathar, Oct 28 2008

Crossrefs

Cf. A095161, A095162, A095163, A095165.

Programs

  • Maple
    A095163 := proc(nmax) local a,dvs,d,n; a := [1,2,3] ; for n from 4 to nmax do dvs := sort(convert(numtheory[divisors](n),list)) ; for d in dvs do if ListTools[Occurrences](d,a) < d then a := [op(a),d] ; break; fi; od: od: a ; end: A095164 := proc(n,a095163) local i ; for i from 1 to nops(a095163) do if op(i,a095163) = n then RETURN(i) ; fi; od: RETURN(-1) ; end: a095163 := A095163(3700) ; for n from 1 do a095 := A095164(n,a095163) ; if a095 < 0 then break; else printf("%d,",a095) ; fi; od: # R. J. Mathar, Oct 28 2008

Extensions

More terms from Nadia Heninger, Jul 07 2005
More terms from R. J. Mathar, Oct 28 2008

A095165 n divided by A095163(n).

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 3, 1, 2, 3, 4, 1, 3, 1, 5, 3, 2, 1, 4, 5, 2, 3, 4, 1, 6, 1, 4, 3, 2, 5, 6, 1, 2, 3, 5, 1, 7, 1, 4, 5, 2, 1, 8, 7, 5, 3, 4, 1, 9, 5, 8, 3, 2, 1, 6, 1, 2, 7, 8, 5, 6, 1, 4, 3, 7, 1, 9, 1, 2, 5, 4, 7, 6, 1, 10, 9, 2, 1, 7, 5, 2, 3, 11, 1, 10, 7, 4, 3, 2, 5, 12, 1, 7, 11, 10, 1, 6
Offset: 1

Views

Author

Amarnath Murthy, Jun 01 2004

Keywords

Comments

Differs from A059981 and A033676 at n = 20. - Franklin T. Adams-Watters, Dec 07 2006

Links

Crossrefs

Cf. A095161, A095162, A095163, A095164.
Cf. A116548.

Programs

Extensions

More terms from Franklin T. Adams-Watters, Dec 07 2006

A095787 Numbers n such that A095163(n) is different from A033677(n).

Original entry on oeis.org

20, 30, 42, 48, 54, 56, 72, 80, 88, 90, 96, 99, 104, 108, 110, 117, 120, 126, 130, 132, 140, 143, 150, 154, 156, 160, 168, 180, 182, 192, 195, 204, 208, 210, 216, 221, 224, 228, 234, 238, 240, 252, 255, 264, 266, 270, 272, 280, 285, 288, 294, 300, 304, 306
Offset: 1

Views

Author

Klaus Brockhaus, Jun 05 2004

Keywords

Comments

A095163(n) <= A033677(n).

Examples

			A095163(54) = 6, A033677(54) = 9, so 54 is in the sequence.
For n = 12 we have divisors 1, 2, 3, 4, 6, 12; 1 occurs earlier once, 2 occurs earlier twice, 3 occurs earlier 3 times, but 4 occurs earlier only once, hence a(12) = 4.

Crossrefs

Cf. A095163, A033677.

Programs

  • PARI
    {m=310;v=vector(m);for(n=1,m,d=divisors(n);j=1;while(v[d[j]]>=d[j],j++);x=d[j];v[d[j]]=v[d[j]]+1;r=sqrt(n);j=1;while(d[j]
  • PARI
    {m=80;v=vector(m);for(n=1,m,d=divisors(n);j=1;while(v[d[j]]>=d[j],j++);print1(d[j],",");v[d[j]]=v[d[j]]+1)}

A116548 a(n) = smallest divisor d of n that occurs earlier in the sequence fewer than a(d) times.

Original entry on oeis.org

1, 2, 3, 2, 5, 3, 7, 4, 3, 5, 11, 4, 13, 7, 5, 8, 17, 6, 19, 5, 7, 11, 23, 6, 5, 13, 9, 7, 29, 6, 31, 8, 11, 17, 7, 9, 37, 19, 13, 8, 41, 7, 43, 11, 9, 23, 47, 8, 7, 10, 17, 13, 53, 18, 11, 14, 19, 29, 59, 10, 61, 31, 21, 16, 13, 11, 67, 17, 23, 10, 71, 12, 73, 37, 15, 19, 11, 13, 79, 10
Offset: 1

Views

Author

Franklin T. Adams-Watters, Mar 16 2006

Keywords

Comments

When n is prime, no smaller divisor is available, so a(n) = n. It can be shown than a(n) < n if n is composite. Similar to Golomb's sequence (A001462), but with the added condition that a(n) divides n.

Links

Crossrefs

Cf. A095163, A001462.

Programs

  • Python
    from sympy import divisors
def A(maxn):
    A = []
    for n in range(1,maxn+1):
        d = divisors(n)
        for j in range(0,len(d)):
            if d[j] > len(A): break
            if A.count(d[j]) < A[d[j]-1]: break
        A.append(d[j])
    return(A) # John Tyler Rascoe, Mar 04 2023

A094173 a(n) = m if m has already occurred at least once and n=k+i*(m+1) where k is the index of the first occurrence of n and i=1,...,max(n-1,1), otherwise a(n) = least positive integer that has not yet occurred.

Original entry on oeis.org

1, 2, 1, 3, 2, 4, 5, 3, 6, 7, 4, 3, 5, 8, 9
Offset: 1

Views

Author

Amarnath Murthy, Jun 01 2004

Keywords

Comments

Is the sequence possible for all n?
a(16) does not exist: it would have to be 4 (since a(6) = a(11) = 4 and so a(6 + 2*(4 + 1)) = a(16) = 4) and also 6 (since a(9) = 6 and so a(9 + 1*(6 + 1)) = a(16) = 6) simultaneously. - Herman Jamke (hermanjamke(AT)fastmail.fm), May 01 2008

Crossrefs

Cf. A095162, A095163, A095164.

Extensions

Edited by Herman Jamke (hermanjamke(AT)fastmail.fm), May 01 2008
Showing 1-5 of 5 results.

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