A135204 -id:A135204 - cp's OEIS frontend

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

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

A135206 Numbers m for which Sum_digits(m!) is a multiple of Sum_digits(m!!).

Original entry on oeis.org

1, 2, 3, 11, 19, 28, 48, 64, 158, 164, 190, 308, 324, 602, 782, 926, 1202, 1540, 1568, 1614, 2076, 2122, 2340, 2546, 2818, 2858, 2866, 3334, 3582, 3714, 4120, 4266, 4794, 5084, 5432, 5454, 5696, 6112, 6250, 6276, 6358, 6760, 7368, 8218, 8970, 9004, 9088

Offset: 1

Paolo P. Lava, Nov 30 2007

			11!=11*10*9*8*7*6*5*4*3*2*1=39916800 -> (3+9+9+1+6+8+0+0)=36,
11!!=11*9*7*5*3*1=10395 -> (1+0+3+9+5)=18,
36/18=2.

Michel Marcus, Table of n, a(n) for n = 1..90

Cf. A004152, A120390, A108825, A129980, A131954, A131955, A135204, A135205.

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(w/x)=w/x then print(i); fi; od; end: P(1000);

Select[Range[1000], Divisible[Total[IntegerDigits[#!, 10]], Total[IntegerDigits[#!!, 10]]] &] (* G. C. Greubel, Sep 30 2016 *)

df(n) = prod(i=0, (n-1)\2, n - 2*i ); \\ A006882
isok(m) = !(sumdigits(m!) % sumdigits(df(m))); \\ Michel Marcus, Jun 18 2024

Changed offset to 1 by Paolo P. Lava, Jun 17 2024

cp's OEIS Frontend

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

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