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A061602
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Sum of factorials of the digits of n.
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44
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1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 2, 2, 3, 7, 25, 121, 721, 5041, 40321, 362881, 3, 3, 4, 8, 26, 122, 722, 5042, 40322, 362882, 7, 7, 8, 12, 30, 126, 726, 5046, 40326, 362886, 25, 25, 26, 30, 48, 144, 744, 5064, 40344, 362904, 121, 121, 122, 126
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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Numbers n such that a(n) = n are known as factorions. It is known that there are exactly four of these [in base 10]: 1, 2, 145, 40585. - Amarnath Murthy
The sum of factorials of the digits is the same for 0, 1, 2 in any base. - Alonso del Arte, Oct 21 2012
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LINKS
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EXAMPLE
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a(24) = (2!) + (4!) = 2 + 24 = 26.
a(153) = 127 because 1! + 5! + 3! = 1 + 120 + 6 = 127.
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MAPLE
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add(factorial(d), d=convert(n, base, 10)) ;
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MATHEMATICA
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a[n_] := Total[IntegerDigits[n]! ]; Table[a[n], {n, 1, 53}] (* Saif Hakim (saif7463(AT)gmail.com), Apr 23 2006 *)
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PROG
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(PARI) { for (n=0, 1000, a=0; x=n; until (x==0, a+=(x - 10*(x\10))!; x=x\10); write("b061602.txt", n, " ", a) ) } \\ Harry J. Smith, Jul 25 2009
(Magma) a061602:=func< n | n eq 0 select 1 else &+[ Factorial(d): d in Intseq(n) ] >; [ a061602(n): n in [0..60] ]; // Klaus Brockhaus, Nov 23 2010
(Python)
import math
s=0
for i in str(n):
s+=math.factorial(int(i))
(R)
i=0
values <- c()
while (i<1000) {
i=i+1
}
plot(values)
sum=0;
numberstring <- paste0(i)
numberstring_split <- strsplit(numberstring, "")[[1]]
for (number in numberstring_split) {
sum = sum+factorial(as.numeric(number))
}
return(sum)
}
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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EXTENSIONS
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Link and amended comment by Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 12 2004
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STATUS
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approved
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