A263025 n is the a(n)-th positive integer having its sum of divisors.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 3, 1, 1, 1, 1, 2, 3, 1, 1, 1, 3, 1, 2, 1, 4, 2, 1, 2, 3, 1, 1, 2, 1, 1, 2, 1, 1, 1, 3, 2, 5, 1, 1, 1, 2, 1, 4, 2, 2, 1, 1, 2, 3, 1, 1, 1, 3

Offset

1,11

Comments

Sum of divisors is given by A000203.

This can also be described as the ordinal transform of A000203. - Franklin T. Adams-Watters, Oct 09 2015

a(n) > 1 iff n is in A069822.

Links

Paul Tek, Table of n, a(n) for n = 1..25000

Formula

a(A034885(k))=1 for k>0.

Example

The numbers with sum of divisors 72 are: 30, 46, 51, 55, 71.
Hence: a(30)=1, a(46)=2, a(51)=3, a(55)=4, a(71)=5.
More generally: the terms of each row of A085790 (say of length i) map to 1, 2, ..., i.
Also: for any n>0, the n terms of the n-th row of A201915 map to 1, 2, ..., n.

Maple

N:= 1000: # to get a(1) to a(N)
Sigmas:= [seq(numtheory:-sigma(i), i=1..N)]:
seq(numboccur(Sigmas[n], Sigmas[1..n]), n=1..N); # Robert Israel, Oct 09 2015

Mathematica

t = DivisorSigma[1, #] & /@ Range@ 10000; s = Position[t, #] & /@ Range@ Max@ t; Flatten[Position[s, #, {3}]][[2]] & /@ Range@ 87 (* Michael De Vlieger, Oct 09 2015 *)

Prog

(PARI) cnt = vector(224); for (n=1, 87, s=sigma(n); cnt[s] = cnt[s]+1; print1(cnt[s] ", "))

Crossrefs

Cf. A000203, A034885, A069822, A078898, A085790, A201915.

Sequence in context: A089048 A329443 A348416 * A184348 A307614 A363057

Adjacent sequences: A263022 A263023 A263024 * A263026 A263027 A263028

Keyword

nonn,look

Author

Paul Tek, Oct 09 2015

Status

approved