A378099 The smallest number whose sum of proper divisors (aliquot parts) is the repunit number A002275(n) = (10^n - 1)/9.

1, 2, 21, 321, 7721, 184729, 185145, 21110729, 54929017, 134099385, 3331670169, 287954234809, 330389987289, 4268122018925, 38011695906145, 196584241823289, 5369335816258145, 33333333333333321, 141084098557734969, 9652121670600495449, 29512417650242257465

Offset

0,2

Comments

For n >= 2, a(n) <= A073046((A002275(n)-1)/2). - Max Alekseyev, Sep 01 2025

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = A070015(A002275(n)). - Max Alekseyev, Aug 31 2025

Example

a(4) = 7721 because 7721 is the smallest number whose sum of proper divisors is A002275(4) = 1111.

Prog

(PARI) a(n) = my(k=1); while (sigma(k)-k != (10^n - 1)/9, k++); k; \\ Michel Marcus, Nov 16 2024

Crossrefs

Cf. A001065, A002275, A070015, A116017, A235710, A244444, A279359, A291373.

Sequence in context: A234525 A230382 A189489 * A196629 A196637 A240997

Adjacent sequences: A378096 A378097 A378098 * A378100 A378101 A378102

Keyword

nonn,hard

Author

Shyam Sunder Gupta, Nov 16 2024

Extensions

a(0)=1 prepended and a(11)-a(20) added by Max Alekseyev, Oct 18 2025

Status

approved