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

Author

Paul Tek, Oct 09 2015

Keywords

• nonn
• look

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.

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)

PARI

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

Formula

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