A085066 -id:A085066 - cp's OEIS frontend

A085067 a(1) = 6, a(n) = smallest number of the form k*a(n-1) + 1 with the same number of divisors, i.e., 4.

6, 55, 111, 334, 335, 671, 1343, 16117, 16118, 64473, 64474, 257897, 2063177, 8252709, 41263546, 123790639, 371371918, 1485487673, 2970975347, 59419506941, 356517041647, 5704272666353, 11408545332707, 262396542652262

Offset: 1

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 29 2003

Though the initial terms match, this sequence differs from A085066, in that the terms can be of two prime signatures, i.e., p*q and p^3 such that tau(p*q) = tau(p^3) = 4.

The claim that these two sequences differ is not yet proved: one would need to demonstrate that there is at least one term of the form p^3 in this sequence. (So far, none of the first 90 entries of the sequence is of that format.) - R. J. Mathar, Aug 27 2025

Amiram Eldar, Table of n, a(n) for n = 1..90

Cf. A085066.

v = 6; Print[v]; Do[k = 1; While[DivisorSigma[0, k*v + 1] != 4, k++ ]; v = k*v + 1; Print[v], {n, 2, 30}] (* Ryan Propper, Aug 29 2005 *)
snsnd[n_]:=Module[{k=1},While[DivisorSigma[0,k*n+1]!=4,k++];k*n+1]; NestList[ snsnd,6,30] (* Harvey P. Dale, Apr 19 2021 *)

Corrected and extended by Ryan Propper, Aug 29 2005

cp's OEIS Frontend

A085067 a(1) = 6, a(n) = smallest number of the form k*a(n-1) + 1 with the same number of divisors, i.e., 4.

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