A386426 Odd nondeficient numbers k such that sigma(k) has the same powerful part as k, where sigma is the sum of divisors function.

81022725, 891360225, 992106225, 1863765225, 2349967725, 3322372725, 7211992725, 8670600225, 9156802725, 11101612725, 13208490225, 15477435225, 15963637725, 18394650225, 18880852725, 21311865225, 21960135225, 22446337725, 22932540225, 25687687725, 25849755225, 28280767725, 28604902725, 30711780225, 31035915225

Offset: 1

Author

Antti Karttunen, Aug 17 2025

Keywords

• nonn
• new

Comments

Sequence by definition contains also any such hypothetical odd terms of A007691 that are mentioned in the comments of A386425. However, if no such terms exist, then this is a subsequence of A386427.

This sequence contains also the intersection of A001694 and A386425, even though it is probably an empty set. See comments in A386428.

The first three terms not divisible by 25 are: a(191) = 283806508293, a(247) = 371184932349, a(328) = 502252568433.

Links

• Giovanni Resta, Table of n, a(n) for n = 1..400
• Index entries for sequences related to sigma(n).
• Index entries for sequences where odd perfect numbers must occur, if they exist at all.

Crossrefs

Intersection of A023196 and A386425.

Conjectured to be a subsequence of A386427.

Cf. A000203, A001694, A003557, A007691, A057521, A386428.

Cf. also A005231.

Programs

PARI

A057521(n)=my(f=factor(n)); prod(i=1, #f~, if(f[i, 2]>1, f[i, 1]^f[i, 2], 1))
isA386426(n) = if(!(n%2), 0, my(s=sigma(n)); ((s>=(2*n)) && (A057521(s)==A057521(n))));

Formula

{k | k is odd, A000203(k) >= 2*k and A003557(A000203(k)) = A003557(k)}.

Extensions

a(8)-a(25) from Giovanni Resta, Aug 18 2025