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A244090 Numbers n such that n is a factorion (A014080, equal to the sum of the factorials of its digits), in at least one base b.

%I A244090 #9 Jul 13 2014 10:27:12
%S A244090 1,2,7,25,26,48,49,121,122,144,145,240,721,722,726,1440,1441,1442,
%T A244090 5041,5042,5162,5760
%N A244090 Numbers n such that n is a factorion (A014080, equal to the sum of the factorials of its digits), in at least one base b.
%C A244090 The bases in which n = func(n) are 2, 2, 4, 6, 6, 11, 5, 24, 24, 28, 10, 47, 120, 120, 240, 239, 15, 15, 720, 720, 27, 822. Note multiple bases for some n, e.g. 25 = 4! + 1! in base 6 and 25 = 1! + 4! in base 21; 721 = 6! + 1! in base 120 and 721 = 1! + 6! in base 715.
%H A244090 Wikipedia, <a href="http://en.wikipedia.org/wiki/Factorion">Factorion</a>
%F A244090 s = 0; for digit(i=1..j) of n in base b, s = s + digit(i)!.
%e A244090 1 = 1! = 1 (base>=2).
%e A244090 2 = 1! + 0! = 1 + 1 = 10 (b=2).
%e A244090 7 = 1! + 3! = 1 + 6 = 13 (b=4).
%e A244090 25 = 4! + 1! = 24 + 1 = 41 (b=6).
%e A244090 26 = 4! + 2! = 24 + 2 = 42 (b=6).
%e A244090 48 = 4! + 4! = 24 + 24 = 44 (b=11).
%e A244090 49 = 1! + 4! + 4! = 1 + 24 + 24 = 144 (b=5).
%e A244090 121 = 5! + 1! = 120 + 1 = 51 (b=24).
%e A244090 122 = 5! + 2! = 120 + 2 = 52 (b=24).
%e A244090 144 = 5! + 4! = 120 + 24 = 54 (b=28).
%e A244090 145 = 1! + 4! + 5! = 1 + 24 + 120 (b=10).
%e A244090 240 = 5! + 5! = 120 + 120 = 55 (b=47).
%o A244090 (PARI) isok(n) = {if (n==1, return (1)); for (b=2, n, d = digits(n, b); if (sum(i=1, #d, d[i]!) == n, return (1));); return (0);} \\ _Michel Marcus_, Jun 21 2014
%Y A244090 Cf. A193163, A014080.
%K A244090 nonn,base,more
%O A244090 1,2
%A A244090 _Anthony Sand_, Jun 20 2014