A348742 Odd numbers k for which A161942(k) >= k, where A161942 is the odd part of sigma.

1, 9, 25, 49, 81, 121, 169, 225, 289, 361, 441, 529, 625, 729, 841, 961, 1089, 1225, 1369, 1521, 1681, 1849, 2025, 2205, 2209, 2401, 2601, 2809, 3025, 3249, 3481, 3721, 3969, 4225, 4489, 4761, 5041, 5329, 5625, 5929, 6241, 6561, 6889, 7225, 7569, 7921, 8281, 8649, 9025, 9409, 9801, 10201, 10609, 11025, 11449, 11881, 12321

Offset: 1

Author

Antti Karttunen, Nov 02 2021

Keywords

• nonn

Comments

All odd squares (A016754) are present, but not all terms are squares. A348743 gives the nonsquare terms.

Odd terms of A336702 form a subsequence. Also all odd terms of A005820 would be present here, as well as any hypothetical quasi-perfect numbers (see comments and references in A332223, A336700), both in A016754. - Antti Karttunen, Nov 28 2024

Links

• Index entries for sequences where odd perfect numbers must occur, if they exist at all
• Index entries for sequences related to sigma(n)

Crossrefs

Union of A016754 and A348743.

Cf. A161942, A162284 (subsequence), A336702, A348741 (complement among the odd numbers).

Cf. also A005820, A332223, A336700, A348739.

Programs

Maple

q:= n-> (t-> is(t/2^padic[ordp](t,2)>=n))(numtheory[sigma](n)):
select(q, [2*i-1$i=1..10000])[];  # Alois P. Heinz, Nov 28 2024

Mathematica

odd[n_] := n/2^IntegerExponent[n, 2]; Select[Range[1, 10^4, 2], odd[DivisorSigma[1, #]] >= # &] (* Amiram Eldar, Nov 02 2021, edited (because of the changed definition) by Antti Karttunen, Nov 28 2024 *)

PARI

A000265(n) = (n >> valuation(n, 2));
isA348742(n) = ((n%2)&&A000265(sigma(n))>=n); \\ revised by Antti Karttunen, Nov 28 2024

Extensions

a(1) = 1 inserted as the initial term, because of the changed definition (from > to >=) - Antti Karttunen, Nov 28 2024