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

Author

Amiram Eldar, Oct 13 2021

Keywords

• nonn

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).

Examples

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

Links

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

Crossrefs

Cf. A036537, A348271, A348345.

Subsequence of A162643.

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

Programs

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] &]