A372575 Lexicographically earliest infinite sequence such that a(i) = a(j) => A276085(i) = A276085(j), for all i, j >= 1, where A276085 is the primorial base log-function.

1, 2, 3, 3, 4, 5, 6, 5, 7, 8, 9, 7, 10, 11, 12, 7, 13, 14, 15, 12, 16, 17, 18, 14, 19, 20, 4, 16, 21, 22, 23, 14, 24, 25, 26, 4, 27, 28, 29, 22, 30, 31, 32, 24, 33, 34, 35, 4, 36, 37, 38, 29, 39, 8, 40, 31, 41, 42, 43, 33, 44, 45, 46, 4, 47, 48, 49, 38, 50, 51, 52, 8, 53, 54, 55, 41, 56, 57, 58, 33, 12, 59, 60, 46, 61, 62, 63, 48, 64, 65, 66, 50, 67, 68, 69, 8

Offset

1,2

Comments

Restricted growth sequence transform of A276085, where A276085 is fully additive with a(p) = A002110(A000720(p)-1).

For all i, j >= 1:

a(i) = a(j) => A035263(i) = A035263(j),

a(i) = a(j) => A369001(i) = A369001(j),

a(i) = a(j) => A372576(i) = A372576(j).

A048103(n) gives the position of the initial occurrence of each n, while A100716 gives the indices of the further occurrences.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to prime indices in the factorization of n

Index entries for sequences related to primorial numbers

Formula

For all n >= 1, a(A048103(n)) = n.

Prog

(PARI)
up_to = 65537;
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; };
A002110(n) = prod(i=1, n, prime(i));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
v372575 = rgs_transform(vector(up_to, n, A276085(n)));
A372575(n) = v372575[n];

Crossrefs

Cf. A000720, A002110, A276085, A035263, A369001, A372576.

Cf. A048103 (positions of records and initial occurrences), A100716.

Cf. also A322815.

Sequence in context: A300587 A075699 A112330 * A332682 A304183 A157222

Adjacent sequences: A372572 A372573 A372574 * A372576 A372577 A372578

Keyword

nonn

Author

Antti Karttunen, May 25 2024

Status

approved