A386427 Odd nondeficient numbers of the form p^(1+4k) * r^2, where p is prime of the form 1+4m, r > 1, and gcd(p,r) = 1.

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

Offset: 1

Author

Antti Karttunen, Aug 18 2025

Keywords

• nonn
• new

Comments

Nondeficient numbers (A023196) that satisfy Euler's condition for odd perfect numbers (A228058).

This is not equal to A348743, as that sequence contains also terms like 1279741205456530915782536871495922949062895982530933679752838870798129159675 and 15388519572341080054329140040512468358441210638435506649120749687401476705908239675, that are lacking from this sequence.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..36000
• 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 A023196 and A228058.

Also the intersection of A083207 and A228058, and probably also of A005835 and A228058. - Antti Karttunen, Aug 21 2025

Subsequence of A348743, from which this eventually differs at some very large n.

Cf. A386426 (conjectured subsequence).

Programs

PARI

isA228058(n) = if(!(n%2)||(omega(n)<2), 0, my(f=factor(n), y=0); for(i=1, #f~, if(1==(f[i, 2]%4), if((1==y)||(1!=(f[i, 1]%4)), return(0), y=1), if(f[i, 2]%2, return(0)))); (y));
isA386427(n) = ((sigma(n)>=(2*n)) && isA228058(n));