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

Author

Antti Karttunen, Mar 08 2021

Keywords

• nonn

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.

Crossrefs

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

Programs

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)));

Formula

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