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

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

Offset: 1

Author

Farideh Firoozbakht, Aug 01 2014

Keywords

• nonn
• base
• more
• hard

Comments

The numbers 47379454926624737751 and 546139199807860751551844463475591 belong to this sequence. - Giovanni Resta, Aug 17 2019

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

Examples

			sigma(4761903)+4761903 = 11111111.
		

Crossrefs

Subsequence of A116017.

Cf. A309835.

Programs

PARI

for(n=1, 10^10, d=digits(sigma(n)+n); if(vecmax(d)==1&&vecmin(d)==1, print1(n, ", "))) \\ 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

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