A037478 Number of positive solutions to "numbers that are n times sum of their digits".
9, 1, 1, 4, 1, 1, 4, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 11, 1, 1, 3, 1, 1, 3, 2, 2, 12, 1, 1, 3, 1, 1, 4, 1, 2, 15, 2, 1, 4, 1, 1, 3, 1, 1, 13, 2, 2, 3, 1, 1, 4, 1, 1, 13, 1, 1, 2, 1, 1, 3, 0, 0, 7, 0, 1, 4, 1, 1, 4, 1, 1, 8, 1, 0, 3, 1, 1, 4, 1, 1, 10, 1, 0, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 0, 1, 3, 1, 1, 9, 1
Offset: 1
Examples
a(13)=3 since the only three solutions are 117=9*13, 156=12*13 and 195=15*13.
Links
- Giovanni Resta, Table of n, a(n) for n = 1..10000
Programs
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Maple
read("transforms"): A037478 := proc(n) local a,x,k; a := 0 ; for k from 1 do x := n*k ; if digsum(x)*n = x then a := a+1 ; end if; # may stop if x/digsum(x)>n, so if x/#digits(x) > 9*n if x/A055642(x) > 9*n then break; end if; end do: a ; end proc: seq(A037478(n),n=1..101) ; # R. J. Mathar, May 11 2016
Comments