A218861 -id:A218861 - cp's OEIS frontend

A066135 a(n) = least number m > 1 such that sigma_n(m) = k*m for some k.

6, 10, 6, 34, 6, 10, 6, 84, 6, 10, 6, 34, 6, 10, 6, 84, 6, 10, 6, 34, 6, 10, 6, 194, 6, 10, 6, 34, 6, 10, 6, 84, 6, 10, 6, 34, 6, 10, 6, 84, 6, 10, 6, 34, 6, 10, 6, 228, 6, 10, 6, 34, 6, 10, 6, 84, 6, 10, 6, 34, 6, 10, 6, 84, 6, 10, 6, 34, 6, 10, 6, 194, 6, 10, 6

Offset: 1

Labos Elemer, Dec 06 2001

nonn

a(n) <= 2p, where p = A002586(n) is the smallest prime factor of (1 + 2^n). (Proof. Since sigma_n(2p) = (1 + 2^n)(1 + p^n) and p is odd, 2p divides sigma_n(2p).) - Jonathan Sondow, Nov 23 2012

T. D. Noe, Table of n, a(n) for n = 1..10000

Cf. A000203, A001157, A001158, A001159, A002586, A007691, A046762-A046764, A055709-A055717.

Cf. A218860, A218861 (unique values and where they first occur).

Table[m = 2; While[Mod[DivisorSigma[n, m], m] > 0, m++]; m, {n, 100}] (* T. D. Noe, Nov 23 2012 *)

Sum{d^n} = ka(n), d runs over the divisors of a(n), where k is an integer and a(n) is the smallest suitable number.

Definition and formulas corrected by Jonathan Sondow, Nov 23 2012

A218860 Unique integers appearing in A066135, in order of appearance.

Original entry on oeis.org

6, 10, 34, 84, 194, 228, 386, 1282, 1538, 3084, 147468, 1956, 1046532, 24578, 3252, 4548, 638978, 5844, 28524, 26626, 229378, 44076, 24636, 59628, 117948, 18804, 75778, 83604, 30468

Offset: 1

T. D. Noe, Nov 24 2012

Cf. A218861 (first position of these numbers in A066135).

f[n_]:=(m = 2; While[Mod[DivisorSigma[n, m], m] > 0, m++]; m); s={}; Do[m=f[n]; If[!MemberQ[s,m],AppendTo[s,m]],{n,1,1000}]; s (* Amiram Eldar, Dec 18 2018 after T. D. Noe at A066135 *)

More terms from Amiram Eldar, Dec 18 2018

cp's OEIS Frontend

A066135 a(n) = least number m > 1 such that sigma_n(m) = k*m for some k.

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