A386429 Odd composites k such that A342926(k) is even and A342926(2*k) is a multiple of 3 and which satisfy Euler's condition for odd perfect numbers (A228058).

45, 153, 261, 325, 369, 405, 477, 801, 909, 925, 1017, 1233, 1341, 1377, 1525, 1557, 1573, 1773, 1825, 2097, 2205, 2313, 2349, 2421, 2425, 2529, 2637, 2725, 2853, 3177, 3321, 3501, 3609, 3645, 3757, 3825, 3925, 4041, 4149, 4293, 4477, 4525, 4581, 4689, 4825, 5013, 5121, 5337, 5445, 5553, 5725, 5733, 5769, 5877, 6025

Offset: 1

Author

Antti Karttunen, Aug 18 2025

Keywords

• nonn
• new

Comments

Sequence contains also some terms of A386428: 28125, 253125, 1378125, 2278125, 3341637, 3403125, 4753125, etc.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences where odd perfect numbers must occur, if they exist at all
• Index entries for sequences related to sigma(n)

Crossrefs

Intersection of A228058 and A347874.

Conjectured to be also the intersection of A228058 and A349751.

Setwise difference A228058 \ A351574.

Cf. also A349755, A387162.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A342926(n) = (A003415(sigma(n))-n);
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));
isA347874(n) = ((n%2)&&!isprime(n)&&!(A342926(n)%2)&&!(A342926(2*n)%3));
isA386429(n) = (isA228058(n) && isA347874(n));