A348743 Odd nonsquares k for which A161942(k) >= k, where A161942 is the odd part of sigma.

2205, 19845, 108045, 143325, 178605, 187425, 236925, 266805, 319725, 353925, 372645, 407925, 452025, 462825, 584325, 637245, 646425, 658125, 672525, 789525, 796005, 804825, 845325, 920205, 972405, 981225, 1007325, 1055925, 1069425, 1102725, 1113525, 1116225, 1166445, 1201725, 1245825, 1289925, 1378125, 1380825, 1442925

Offset: 1

Author

Antti Karttunen, Nov 02 2021

Keywords

• nonn
• changed

Comments

The first non-multiples of 5 are a(103) = 6243237 and a(125) = 8164233.

From Antti Karttunen, Nov 28 2024: (Start)

This is not a subsequence of A228058. At least k = A000040(28)*(A002110(27)/2)^2 = 15388519572341080054329140040512468358441210638435506649120749687401476705908239675 is a number of the form 4m+3 such that A161942(k) >= k.

Another such number is A000040(28)*81*(A002110(25)/6)^2 = 1279741205456530915782536871495922949062895982530933679752838870798129159675.

Question: What is the smallest term of this sequence that is of the form 4m+3, and thus not in A386427 (in A191218 and in A228058)?

(End)

Links

• Antti Karttunen, Table of n, a(n) for n = 1..55135; terms <= 10^10
• Index entries for sequences where odd perfect numbers must occur, if they exist at all
• Index entries for sequences which agree for a long time but are different
• Index entries for sequences related to sigma(n)

Crossrefs

Intersection of A088828 and A348742.

Cf. A386427 (a subsequence, which agrees for a very long time).

Cf. A033630, A065205, A083206, A161942, A191218, A228058, A336702, A348741.

Cf. also A065235, A162284.

Programs

PARI

A000265(n) = (n >> valuation(n, 2));
isA348743(n) = ((n%2)&&!issquare(n)&&A000265(sigma(n))>=n); \\ Edited Nov 28 2024

Extensions

Definition changed (from > to >=) to formally include also any hypothetical odd perfect numbers - Antti Karttunen, Nov 28 2024

Comment removed, because it was more related to sequence A386427. - Antti Karttunen, Aug 21 2025