A084034 Numbers which are a product of repeated-digit numbers A010785.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 49, 50, 54, 55, 56, 60, 63, 64, 66, 70, 72, 75, 77, 80, 81, 84, 88, 90, 96, 98, 99, 100, 105, 108, 110, 111, 112, 120, 121, 125, 126, 128

Offset: 1

Author

Amarnath Murthy, May 26 2003

Keywords

• base
• nonn

Comments

Numbers which can be written as a*b*c*... where a, b, c are numbers whose decimal expansions are repetitions of a single digit.

Superset of A051038. The first numbers in this sequence but not in A051038 are 111, 222, 333, 444, 555. - R. J. Mathar, Sep 17 2008

From David A. Corneth, Aug 03 2017: (Start)

Closed under multiplication.

Multiples of 1-digit primes and numbers of the form (10^n - 1) / 9. (End)

Examples

			99 is a member since 99 = 3*33.
9768 is a member since 9768= 2*22*222.
111*2*33*44 = 322344 is a member.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..12917 (Terms <= 10^8)

Crossrefs

Cf. A002275, A010785, A051038, A084348.

A002473 gives products of single-digit numbers.

Programs

Maple

isA010786 := proc(n) if nops(convert(convert(n,base,10),set)) = 1 then true; else false ; fi; end: isA084034 := proc(n,a010785) local d ; if n = 1 then RETURN(true) ; fi; for d in ( numtheory[divisors](n) minus{1} ) do if d in a010785 then if isA084034(n/d,a010785) then RETURN(true) ; fi; fi; od: RETURN(false) ; end: nmax := 1000: a010785 := [] : for k from 1 to nmax do if isA010786(k) then a010785 := [op(a010785),k] ; fi; od: for n from 1 to nmax do if isA084034(n,a010785) then printf("%d,",n) ; fi; end: # R. J. Mathar, Sep 17 2008

Extensions

Corrected and extended by David Wasserman, Dec 09 2004

Corrected data, offset changed to 1 by David A. Corneth, Aug 03 2017

Edited by N. J. A. Sloane, Jul 02 2017 and Oct 10 2018