A061602 Sum of factorials of the digits of n.

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

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

Cf. A061603, A108911, A193163, A165451 (places of primes).

See also A014080, A214285, A254499, A306955.

Sequence in context: A066459 A269221 A071937 * A182287 A248778 A033647

Adjacent sequences: A061599 A061600 A061601 * A061603 A061604 A061605

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