A244444 Numbers k such that k+sigma(k) is a repunit number.

4, 5, 506311, 4761903, 506767303, 5517762660583, 5554746531623, 5555541480743, 5458110152757191, 45171625279943274951, 47379454926624737751

Offset

1,1

Comments

The number 546139199807860751551844463475591 belongs to this sequence. - Giovanni Resta, Aug 17 2019

Also in the sequence is 38808343270779723425176258917550576371890625326889683884600092615. - Daniel Suteu, Aug 23 2019

The following are also terms: 42253521126760563380281690140845070421983, 484912468871110034058062882695085908065763399, 5555416315084477193803242075128588575040867078261499174304006505314808781061058111. - Daniel Suteu, Mar 14 2026

Links

Table of n, a(n) for n=1..11.

Example

sigma(4761903)+4761903 = 11111111.

Prog

(PARI) isok(n) = my(d=digits(sigma(n)+n)); (vecmax(d)==1) && (vecmin(d)==1); \\ Derek Orr, Aug 02 2014
(Python) from sympy import divisors
[n for n in range(1, 10**6) if len(set(str(n+sum(divisors(n))))) == 1 and str(n+sum(divisors(n)))[0] == '1'] # Chai Wah Wu, Aug 04 2014

Crossrefs

Subsequence of A116017.

Cf. A155085, A309835.

Sequence in context: A058916 A064612 A299639 * A231407 A005927 A201529

Adjacent sequences: A244441 A244442 A244443 * A244445 A244446 A244447

Keyword

nonn,base,more,hard

Author

Farideh Firoozbakht, Aug 01 2014

Extensions

a(5) from Hiroaki Yamanouchi, Aug 26 2014

a(6)-a(8) from Giovanni Resta, Aug 17 2019

a(9) from Daniel Suteu confirmed by Max Alekseyev, May 23 2025

a(11) from Giovanni Resta confirmed and a(10) added by Max Alekseyev, Feb 18 2026

Status

approved