A342011 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), for all i, j >= 1, with f(1) = 2 and f(n) = A004490(n)/A004490(n-1) when n > 1, where A004490(n) is the n-th colossally abundant number.

1, 2, 1, 3, 1, 2, 4, 1, 5, 6, 1, 2, 3, 7, 8, 9, 1, 10, 11, 4, 2, 12, 13, 14, 1, 15, 16, 17, 3, 18, 19, 20, 21, 5, 22, 1, 23, 2, 24, 25, 6, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 35, 36, 4, 37, 38, 39, 7, 40, 41, 42, 43, 44, 45, 46, 8, 47, 2, 48, 49, 50, 3, 51, 52, 53, 54, 1, 55, 56, 57, 58, 59, 60, 61, 62, 9, 63, 64

Offset

1,2

Comments

This is also the restricted growth sequence transform of A073751, provided that quotient A004490(1+n)/A004490(n) is always prime, which is implied by a conjecture mentioned in Lagarias' paper. Note that the b-file of A073751 is computed based on the knowledge that the conjecture holds at least for the first 10^7 quotients.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000 (computed from the b-file of A073751 provided by T. D. Noe)

J. C. Lagarias, An elementary problem equivalent to the Riemann hypothesis, arXiv:math/0008177 [math.NT], 2000-2001; Am. Math. Monthly 109 (#6, 2002), 534-543.

Formula

a(n) = A000720(A073751(n)), up to the first n where A004490(n)/A004490(n-1) is not a prime.

Prog

(PARI)
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };
v073751 = readvec("b073751_to.txt"); \\ Prepared with gawk '{ print $2 }' < b073751.txt > b073751_to.txt
v342011 = rgs_transform(v073751);
A342011(n) = v342011[n];
for(n=1, #v342011, write("b342011.txt", n, " ", A342011(n)));

Crossrefs

Cf. A000720, A004490, A073751, A342010, A342012, A342013.

Sequence in context: A319847 A334217 A334431 * A087295 A175344 A056951

Adjacent sequences: A342008 A342009 A342010 * A342012 A342013 A342014

Keyword

nonn

Author

Antti Karttunen, Mar 08 2021

Status

approved