A347872 Numbers k such that k and A003415(sigma(k)) have the same parity.

5, 6, 8, 9, 12, 13, 14, 17, 18, 22, 24, 25, 28, 29, 30, 36, 37, 38, 41, 42, 44, 45, 46, 48, 50, 53, 54, 56, 60, 61, 62, 66, 70, 73, 76, 78, 84, 86, 88, 89, 92, 94, 96, 97, 100, 101, 102, 108, 109, 110, 112, 113, 114, 117, 118, 120, 124, 126, 130, 132, 134, 137, 138, 140, 142, 144, 149, 150, 152, 153, 154, 156, 157

Offset: 1

Author

Antti Karttunen, Sep 17 2021

Keywords

• nonn

Comments

Numbers k for which A347870(k) is equal to A000035(k).

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index entries for sequences where odd perfect numbers must occur, if they exist at all

Crossrefs

Cf. A000035, A000203, A003415, A342925, A347870.

Positions of zeros in A347871. Cf. A347873 for complement.

Cf. A000396, A342922, A347874 (subsequences).

Cf. also A347883.

Programs

Maple

ader:= proc(n) local F,t;
  F:= ifactors(n)[2];
  add(t[2]*n/t[1], t= F)
end proc:
filter:= n -> n - ader(numtheory:-sigma(n)) mod 2 = 0:
select(filter, [$1..1000]); # Robert Israel, Sep 11 2024

Mathematica

ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); Select[Range[157], Mod[ad[DivisorSigma[1, #]], 2] == Mod[#, 2] &] (* Amiram Eldar, Sep 18 2021 *)