A095165 -id:A095165 - cp's OEIS frontend

A095163 a(n) = smallest divisor d of n that occurs earlier in the sequence fewer than d times.

1, 2, 3, 2, 5, 3, 7, 4, 3, 5, 11, 4, 13, 7, 5, 4, 17, 6, 19, 4, 7, 11, 23, 6, 5, 13, 9, 7, 29, 5, 31, 8, 11, 17, 7, 6, 37, 19, 13, 8, 41, 6, 43, 11, 9, 23, 47, 6, 7, 10, 17, 13, 53, 6, 11, 7, 19, 29, 59, 10, 61, 31, 9, 8, 13, 11, 67, 17, 23, 10, 71, 8, 73, 37, 15, 19, 11, 13, 79, 8, 9, 41, 83

Offset: 1

Amarnath Murthy, Jun 01 2004

nonn

Agrees with A033677 for the first 19 and many further terms; A095787 gives those n for which A033677 and the present sequence disagree.

			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.

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Cf. A033677, A095787, A095161, A095162, A095164, A095165.

nn = 120; c[] = 0; Do[k = SelectFirst[Divisors[n], c[#] < # &]; a[n] = k; c[k]++, {n, nn}]; Array[a, nn] (* _Michael De Vlieger, Oct 14 2022 *)

{m=83;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)}

from sympy import divisors
from collections import Counter
from itertools import count, islice
def agen():
    c = Counter()
    for n in count(1):
        an = next(d for d in divisors(n) if c[d] < d)
        c[an] += 1
        yield an
print(list(islice(agen(), 83))) # Michael S. Branicky, Oct 14 2022

a(n) >= n^(1/3). - Charles R Greathouse IV, Oct 14 2022

Edited and extended by Klaus Brockhaus Jun 05 2004 and Jun 09 2004

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

Amarnath Murthy, Jun 01 2004

nonn

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

Cf. A095161, A095162, A095163, A095165.

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

More terms from Nadia Heninger, Jul 07 2005

More terms from R. J. Mathar, Oct 28 2008

cp's OEIS Frontend

A095163 a(n) = smallest divisor d of n that occurs earlier in the sequence fewer than d times.

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