A097655
Numbers n such that n = d_1!!*d_2!!*...*d_k!! where d_1 d_2 ... d_k is the decimal expansion of n.
Original entry on oeis.org
1, 2, 3, 15, 18432, 75600, 276531978240000, 4810168001497883738112000, 215788176336727572480000000, 2178419737991700039289327133392896000000000000
Offset: 1
18432 is in the sequence because 18432 = 1!!*8!!*4!!*3!!*2!!.
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Do[h=IntegerDigits[n];l=Length[h];If[n==Product[h[[k]]!!, {k, l}], Print[n]], {n, 2000000000}]
A173573
3-Factorions: equal to the sum of the triple factorials of their digits in base 10.
Original entry on oeis.org
1, 2, 3, 4, 81, 82, 83, 84
Offset: 1
81 -> 8!!! + 1!!! = 8*5*2 + 1 = 80 + 1 = 81.
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P:=proc(n,m) local a,b,i,j,k,x,w; for i from 1 by 1 to n do a:=0; b:=0; w:=0; k:=i; while k>0 do w:=k-(trunc(k/10)*10); j:=w; x:=w-m; if w=0 then b:=1; else while x>0 do j:=j*x; x:=x-m; od; b:=j; fi; a:=a+b; k:=trunc(k/10); od; if a=i then lprint(i,a); fi; od; end: P(1000,3);
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stfQ[n_]:=n==Total[Times@@Range[#,1,-3]&/@IntegerDigits[n]]; Select[Range[100],stfQ] (* Harvey P. Dale, May 31 2023 *)
A173577
7-Factorions: equal to the sum of the 7-fold factorials of their digits in base 10.
Original entry on oeis.org
1, 2, 3, 4, 5, 6, 7, 8, 19
Offset: 1
19 -> 1!!!!!!! + 9!!!!!!! = 1 + 9*2 = 1 + 18 = 19.
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P:=proc(n,m) local a,b,i,j,k,x,w; for i from 1 by 1 to n do a:=0; b:=0; w:=0; k:=i; while k>0 do w:=k-(trunc(k/10)*10); j:=w; x:=w-m; if w=0 then b:=1; else while x>0 do j:=j*x; x:=x-m; od; b:=j; fi; a:=a+b; k:=trunc(k/10); od; if a=i then lprint(i,a); fi; od; end: P(1000,7);
A097654
Numbers n such that n=|d_1!!-d_2!!+...+(-1)^(k-1)*d_k!!| where d_1 d_2 ... d_k is the decimal expansion of n.
Original entry on oeis.org
380 is in the sequence because 380=|3!!-8!!+0!!|.
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Do[h=IntegerDigits[n];l=Length[h];If[n==Abs[Sum[(-1)^(k-1) *h[[k]]!!, {k, l}]], Print[n]], {n, 4*9!!}]
A173574
4-Factorions: equal to the sum of the quadruple factorials of their digits in base 10.
Original entry on oeis.org
1, 2, 3, 4, 5, 49
Offset: 1
49 -> 4!!!! + 9!!!! = 4 + 9*5 = 4 +45 = 49.
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P:=proc(n,m) local a,b,i,j,k,x,w; for i from 1 by 1 to n do a:=0; b:=0; w:=0; k:=i; while k>0 do w:=k-(trunc(k/10)*10); j:=w; x:=w-m; if w=0 then b:=1; else while x>0 do j:=j*x; x:=x-m; od; b:=j; fi; a:=a+b; k:=trunc(k/10); od; if a=i then lprint(i,a); fi; od; end: P(1000,4);
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qfd[n_]:=Times@@Range[n,1,-4]; Select[Range[50],Total[qfd/@ IntegerDigits[ #]] == #&] (* Harvey P. Dale, Dec 15 2018 *)
A173575
5-Factorions: equal to the sum of the quintuple factorials of their digits in base 10.
Original entry on oeis.org
1, 2, 3, 4, 5, 6, 39
Offset: 1
39 -> 3!!!!! + 9!!!!! = 3 + 9*4 = 3 + 36 = 39.
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P:=proc(n,m) local a,b,i,j,k,x,w; for i from 1 by 1 to n do a:=0; b:=0; w:=0; k:=i; while k>0 do w:=k-(trunc(k/10)*10); j:=w; x:=w-m; if w=0 then b:=1; else while x>0 do j:=j*x; x:=x-m; od; b:=j; fi; a:=a+b; k:=trunc(k/10); od; if a=i then lprint(i,a); fi; od; end: P(1000,5);
A173576
6-Factorions: equal to the sum of the 6-ple factorials of their digits in base 10.
Original entry on oeis.org
1, 2, 3, 4, 5, 6, 7, 29
Offset: 1
29 -> 2!!!!!! + 9!!!!!! = 2 + 9*3 = 2 + 27 = 29.
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P:=proc(n,m) local a,b,i,j,k,x,w; for i from 1 by 1 to n do a:=0; b:=0; w:=0; k:=i; while k>0 do w:=k-(trunc(k/10)*10); j:=w; x:=w-m; if w=0 then b:=1; else while x>0 do j:=j*x; x:=x-m; od; b:=j; fi; a:=a+b; k:=trunc(k/10); od; if a=i then lprint(i,a); fi; od; end: P(1000,6);
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