A108911 -id:A108911 - cp's OEIS frontend

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

Amarnath Murthy, May 19 2001

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

			a(24) = (2!) + (4!) = 2 + 24 = 26.
a(153) = 127 because 1! + 5! + 3! = 1 + 120 + 6 = 127.

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.

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

See also A014080, A214285, A254499, A306955.

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

A061602 := proc(n)
        add(factorial(d),d=convert(n,base,10)) ;
end proc: # R. J. Mathar, Dec 18 2011

a[n_] := Total[IntegerDigits[n]! ]; Table[a[n], {n, 1, 53}] (* Saif Hakim (saif7463(AT)gmail.com), Apr 23 2006 *)

a(n) = { if(n==0, 1, my(d=digits(n)); sum(i=1, #d, d[i]!)) } \\ Harry J. Smith, Jul 25 2009

import math
def A061602(n):
    s=0
    for i in str(n):
        s+=math.factorial(int(i))
    return s # Indranil Ghosh, Jan 11 2017

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

Corrected and extended by Vladeta Jovovic, May 19 2001

Link and amended comment by Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 12 2004

A111095 n = Sum_{b} c_b*b! in the factorial base rewritten by c_b-fold repetition of b, b=1,2,3,....

Original entry on oeis.org

1, 2, 12, 22, 122, 3, 13, 23, 123, 223, 1223, 33, 133, 233, 1233, 2233, 12233, 333, 1333, 2333, 12333, 22333, 122333, 4, 14, 24, 124, 224, 1224, 34, 134, 234, 1234, 2234, 12234, 334, 1334, 2334, 12334, 22334

Offset: 1

Giorgio Balzarotti and Paolo P. Lava, Oct 13 2005

The integer n has a unique "greedy" representation in the factorial base as n = Sum_{b>=1} c_b*b!, see A007623.
The number of coefficients c_b is A084558(n).
The current sequence starts from an empty string, scans the coefficients c_b in the order b=1,2,3,..., i.e., reads A007623(n) from the least to the most significant position, and appends b c_b times to the string. The resulting string is shown in the sequence as a standard decimal number a(n).

			a(39) = 12334 with A007623(39) = 1211, because 1! + 2! + 3! + 3! + 4! = 1 + 2 + 6 + 6 + 24 = 39

Cf. A005096, A007623, A108911.

A061602(a(n)) = n. - R. J. Mathar, Oct 30 2010

Definition and comment shortened with reference to A007623 - R. J. Mathar, Oct 30 2010

A108933 Numbers n such that the absolute value of (n - sum of the factorials of its digits) is prime.

Original entry on oeis.org

3, 14, 20, 24, 25, 30, 37, 43, 50, 53, 59, 60, 67, 73, 79, 80, 97, 100, 105, 110, 115, 124, 125, 134, 138, 146, 151, 152, 158, 171, 172, 198, 201, 202, 225, 227, 235, 243, 249, 250, 255, 259, 260, 265, 295, 301, 302, 306, 314, 318, 320, 325, 327, 330, 343, 347

Offset: 1

Jason Earls, Jul 20 2005

6*10^843-1 generates an 844-digit prime.

			a(5)=25 because |25-(2!+5!)| = 97, a prime.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A108911.

Select[Range[400],PrimeQ[Abs[#-Total[IntegerDigits[#]!]]]&] (* Harvey P. Dale, Oct 03 2017 *)

A241404 Sum of n and the sum of the factorials of its digits.

Original entry on oeis.org

2, 4, 9, 28, 125, 726, 5047, 40328, 362889, 12, 13, 15, 20, 39, 136, 737, 5058, 40339, 362900, 23, 24, 26, 31, 50, 147, 748, 5069, 40350, 362911, 37, 38, 40, 45, 64, 161, 762, 5083, 40364, 362925, 65, 66, 68, 73, 92, 189, 790, 5111, 40392, 362953, 171, 172, 174

Offset: 1

Vincenzo Librandi, Apr 21 2014

			a(8) = 40328 because we have 8 + 8! = 40328.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A061602, A108911.

f[n_]:= n + Plus@@Factorial/@IntegerDigits[n]; Table[f[n], {n, 50}]

a(n) = my(d = digits(n)); n + sum(i=1, #d, d[i]!); \\ Michel Marcus, Apr 21 2014

a(n) = n + A061602(n). - Michel Marcus, Apr 21 2014

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A061602 Sum of factorials of the digits of n.

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A111095 n = Sum_{b} c_b*b! in the factorial base rewritten by c_b-fold repetition of b, b=1,2,3,....

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A108933 Numbers n such that the absolute value of (n - sum of the factorials of its digits) is prime.

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A241404 Sum of n and the sum of the factorials of its digits.

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Mathematica

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