A218860 -id:A218860 - cp's OEIS frontend

A218861 First position of A218860(n) in A066135.

1, 2, 4, 8, 24, 48, 144, 288, 576, 1152, 2304, 3456, 4608, 9216, 11520, 16128, 18432, 20736, 25344, 29952, 36864, 39168, 43776, 52992, 59904, 66816, 85248, 99072, 108288

Offset: 1

T. D. Noe, Nov 24 2012

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

More terms from Amiram Eldar, Dec 18 2018

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

Original entry on oeis.org

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

cp's OEIS Frontend

A218861 First position of A218860(n) in A066135.

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

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