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

1,2

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

Table of n, a(n) for n=1..57.

Index entries for sequences where odd perfect numbers must occur, if they exist at all

Index entries for sequences related to sigma(n)

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 *)

Prog

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

Crossrefs

Union of A016754 and A348743.

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

Cf. also A005820, A332223, A336700, A348739.

Sequence in context: A113659 A325701 A113745 * A016754 A110487 A377654

Adjacent sequences: A348739 A348740 A348741 * A348743 A348744 A348745

Keyword

nonn

Author

Antti Karttunen, Nov 02 2021

Extensions

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

Status

approved