A347769 a(0) = 0; a(1) = 1; for n > 1, a(n) = A001065(a(n-1)) = sigma(a(n-1)) - a(n-1) (the sum of aliquot parts of a(n-1)) if this is not yet in the sequence; otherwise a(n) is the smallest number missing from the sequence.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 15, 13, 14, 17, 18, 21, 19, 20, 22, 23, 24, 36, 55, 25, 26, 27, 28, 29, 30, 42, 54, 66, 78, 90, 144, 259, 45, 33, 31, 32, 34, 35, 37, 38, 39, 40, 50, 43, 41, 44, 46, 47, 48, 76, 64, 63, 49, 51, 52, 53, 56, 57, 58, 59, 60, 108, 172
Offset: 0
Keywords
Examples
a(0) = 0, a(1) = 1; since A001065(a(1)) = 0 has already appeared in this sequence, a(2) = 2; since A001065(a(2)) = 1 has already appeared in this sequence, a(3) = 3; ... a(11) = 11; since A001065(a(11)) = 1 has already appeared in this sequence, a(12) = 12; since A001065(a(12)) = 16 has not yet appeared in this sequence, a(13) = A001065(a(12)) = 16; since A001065(a(13)) = 15 has not yet appeared in this sequence, a(14) = A001065(a(13)) = 15; since A001065(a(14)) = 9 has already appeared in this sequence, a(15) = 13; ...
Links
- Eric Chen, Table of n, a(n) for n = 0..2703 (all currently known terms, after the b-file of A008892)
- Eric Weisstein's World of Mathematics, Aliquot sequence
- Eric Weisstein's World of Mathematics, Catalan's Aliquot Sequence Conjecture
- Wikipedia, Aliquot sequence
Crossrefs
Cf. A032451.
Cf. A001065 (sum of aliquot parts).
Cf. A007906.
Cf. A115060 (maximum term of aliquot sequences).
Cf. A115350 (termination of the aliquot sequences).
Aliquot sequences starting at various numbers: A000004 (0), A000007 (1), A033322 (2), A010722 (6), A143090 (12), A143645 (24), A010867 (28), A008885 (30), A143721 (38), A008886 (42), A143722 (48), A143723 (52), A008887 (60), A143733 (62), A143737 (68), A143741 (72), A143754 (75), A143755 (80), A143756 (81), A143757 (82), A143758 (84), A143759 (86), A143767 (87), A143846 (88), A143847 (96), A143919 (100), A008888 (138), A008889 (150), A008890 (168), A008891 (180), A203777 (220), A008892 (276), A014360 (552), A014361 (564), A074907 (570), A014362 (660), A269542 (702), A045477 (840), A014363 (966), A014364 (1074), A014365 (1134), A074906 (1521), A143930 (3630), A072891 (12496), A072890 (14316), A171103 (46758), A072892 (1264460).
Programs
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PARI
A347769_list(N)=print1(0, ", "); if(N>0, print1(1, ", ")); v=[0, 1]; b=1; for(n=2, N, if(setsearch(Set(v), sigma(b)-b), k=1; while(k<=n, if(!setsearch(Set(v), k), b=k; k=n+1, k++)), b=sigma(b)-b); print1(b, ", "); v=concat(v, b))
Comments