OFFSET
0,3
COMMENTS
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
LINKS
Harry J. Smith and Indranil Ghosh, Table of n, a(n) for n = 0..10000 (first 1001 terms from Harry J. Smith)
Project Euler, Problem 74: Digit factorial chains
H. J. J. te Riele, Iteration of number-theoretic functions, Nieuw Archief v. Wiskunde, (4) 1 (1983), 345-360. See Example I.1.b.
Eric Weisstein's World of Mathematics, Factorion.
EXAMPLE
a(24) = (2!) + (4!) = 2 + 24 = 26.
a(153) = 127 because 1! + 5! + 3! = 1 + 120 + 6 = 127.
MAPLE
A061602 := proc(n)
add(factorial(d), d=convert(n, base, 10)) ;
end proc: # R. J. Mathar, Dec 18 2011
MATHEMATICA
a[n_] := Total[IntegerDigits[n]! ]; Table[a[n], {n, 1, 53}] (* Saif Hakim (saif7463(AT)gmail.com), Apr 23 2006 *)
PROG
(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
def A061602(n):
s=0
for i in str(n):
s+=math.factorial(int(i))
return s # Indranil Ghosh, Jan 11 2017
(R)
i=0
values <- c()
while (i<1000) {
values[i+1] <- A061602(i)
i=i+1
}
plot(values)
A061602 <- function(n) {
sum=0;
numberstring <- paste0(i)
numberstring_split <- strsplit(numberstring, "")[[1]]
for (number in numberstring_split) {
sum = sum+factorial(as.numeric(number))
}
return(sum)
}
# Raphaël Deknop, Nov 08 2021
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Amarnath Murthy, May 19 2001
EXTENSIONS
Corrected and extended by Vladeta Jovovic, May 19 2001
Link and amended comment by Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 12 2004
STATUS
approved