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A344593 Lexicographically earliest infinite sequence such that a(i) = a(j) => A344592(i) = A344592(j), for all i, j >= 1. 4
1, 1, 1, 2, 1, 3, 1, 1, 1, 4, 1, 5, 1, 6, 7, 8, 1, 9, 1, 10, 11, 12, 1, 13, 14, 15, 1, 16, 1, 17, 1, 1, 18, 19, 20, 21, 1, 22, 23, 1, 1, 1, 1, 24, 25, 26, 1, 27, 18, 28, 29, 30, 1, 31, 32, 33, 34, 35, 1, 36, 1, 37, 38, 39, 40, 41, 1, 42, 43, 44, 1, 45, 1, 46, 47, 48, 49, 50, 1, 51, 11, 52, 1, 53, 54, 55, 56, 57, 1, 58, 59, 60, 61, 62, 63, 64, 1, 65, 66, 11, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
Restricted growth sequence transform of A344592, where A344592(n) = A003557(A276086(A108951(n))).
For all i, j: a(i) = a(j) => A329344(i) = A329344(j).
LINKS
EXAMPLE
Both a(14) = 6 and a(32768) = 6, because A344592(14) = 11 is the sixth distinct value occurring in A344592, and A344592(32768) = A003557(A276086(A108951(32768))) = A003557(A276086(32768)) = A003557(401115) = A003557(3 * 5 * 11^2 * 13 * 17) = 11 also, which is the second time 11 occurs in A344592.
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; };
A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) }; \\ From A108951
A328572(n) = { my(m=1, p=2); while(n, if(n%p, m *= p^((n%p)-1)); n = n\p; p = nextprime(1+p)); (m); };
v344593 = rgs_transform(vector(up_to, n, A344592(n)));
A344593(n) = v344593[n];
CROSSREFS
Cf. A003557, A108951, A276086, A324886, A329344, A344591 (positions of ones), A344592.
Cf. also A329045, A329345, A344594.
Sequence in context: A333768 A306922 A331181 * A353278 A328917 A265917
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 26 2021
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)