A348346 Numbers k such that k and k+1 have the same positive sum of noninfinitary divisors (A348271).

20150, 52767, 99296, 835515, 1241504, 2199392, 6294015, 11158496, 12770450, 17016416, 19127907, 20128544, 23686748, 24790688, 26580554, 33366015, 34385247, 39687651, 42106976, 44157087, 45466676, 59825349, 60832449, 73780244, 75268775, 81654650, 84696849, 111457213

Offset

1,1

Comments

Numbers k such that A348271(k) = A348271(k+1) > 0.

The terms are restricted to have a positive sum of noninfinitary divisors, since there are many consecutive numbers without noninfinitary divisors (these are the terms of A036537).

Links

Amiram Eldar, Table of n, a(n) for n = 1..154

Example

20150 is a term since A348271(20150) = A348271(20151) = 6720.

Mathematica

f[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ f @@@ FactorInteger[n]; s[n_] := DivisorSigma[1, n] - isigma[n]; Select[Range[10^5], (s1 = s[#]) > 0 && s1 == s[# + 1] &]

Crossrefs

Cf. A036537, A348271, A348345.

Subsequence of A162643.

Similar sequences: A002961, A064115, A064125, A293183, A306985.

Sequence in context: A186480 A204864 A353034 * A145535 A190474 A109479

Adjacent sequences: A348343 A348344 A348345 * A348347 A348348 A348349

Keyword

nonn

Author

Amiram Eldar, Oct 13 2021

Status

approved