A135206 -id:A135206 - cp's OEIS frontend

A135204 Numbers n for which Sum_digits(n!) is a multiple of Sum_digits(n).

1, 2, 3, 9, 10, 11, 12, 14, 16, 18, 20, 21, 22, 27, 28, 30, 33, 35, 36, 44, 45, 51, 54, 60, 61, 63, 72, 75, 81, 87, 90, 99, 100, 102, 105, 108, 111, 114, 117, 120, 126, 130, 135, 143, 144, 153, 158, 162, 165, 171, 180, 182, 185, 189, 190, 192, 200, 201, 202, 204, 206

Offset: 1

Paolo P. Lava and Giorgio Balzarotti, Nov 30 2007

I expect a(n) to be around kn log n for some constant k. - Charles R Greathouse IV, Apr 24 2013

			11 -> 11*10*9*8*7*6*5*4*3*2*1=39916800 -> (3+9+9+1+6+8+0+0)/(1+1)=18.

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A004152, A120390, A108825, A129980, A131954, A131955, A135205, A135206.

P:=proc(n) local i,k,w,x; for i from 1 by 1 to n do w:=0; k:=i; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; x:=0; k:=i!; while k>0 do x:=x+k-(trunc(k/10)*10); k:=trunc(k/10); od; if trunc(x/w)=x/w then print(i); fi; od; end: P(1000);

Select[Range[100], Divisible[Total[IntegerDigits[#!, 10]], Total[IntegerDigits[#, 10]]] &] (* G. C. Greubel, Sep 30 2016 *)

is(n)=sumdigits(n!)%sumdigits(n)==0 \\ Charles R Greathouse IV, Apr 24 2013

A135205 Numbers m for which Sum_digits(m!!) is a multiple of Sum_digits(m).

Original entry on oeis.org

1, 2, 3, 4, 6, 9, 10, 11, 12, 15, 18, 20, 21, 24, 25, 27, 30, 32, 33, 36, 42, 45, 46, 54, 55, 63, 72, 75, 81, 88, 90, 91, 93, 100, 101, 102, 105, 108, 111, 112, 117, 120, 121, 122, 123, 124, 126, 127, 135, 141, 144, 153, 154, 156, 162, 171, 176, 180, 182, 189, 198

Offset: 1

Paolo P. Lava, Nov 30 2007

			11 -> 11*9*7*5*3*1=10395 -> (1+0+3+9+5)/(1+1) = 9.

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A004152, A120390, A108825, A129980, A131954, A131955, A135204, A135206.

P:=proc(n) local i,j,k,w,x; for i from 1 by 1 to n do w:=0; k:=i; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; x:=i; j:=i-2; while j >0 do x:=x*j; j:=j-2; od: k:=x; x:=0; while k>0 do x:=x+k-(trunc(k/10)*10); k:=trunc(k/10); od; if trunc(x/w)=x/w then print(i); fi; od; end: P(1000);

Select[Range[100], Divisible[Total[IntegerDigits[#!!, 10]], Total[IntegerDigits[#, 10]]] &] (* G. C. Greubel, Sep 30 2016 *)

Offset 1 and b-file adapted by Paolo P. Lava, Jun 17 2024

cp's OEIS Frontend

A135204 Numbers n for which Sum_digits(n!) is a multiple of Sum_digits(n).

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