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 A061602 Sum of factorials of the digits of n. 44
 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)
 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, "")[] 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

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Last modified September 24 16:22 EDT 2023. Contains 365579 sequences. (Running on oeis4.)