A351949 - OEIS

A351949

Lexicographically earliest infinite sequence such that a(i) = a(j) => A246277(A329044(i)) = A246277(A329044(j)) and A003557(i) = A003557(j), for all i, j >= 1.

1, 2, 2, 3, 2, 4, 2, 5, 6, 4, 2, 7, 2, 4, 8, 9, 2, 10, 2, 7, 8, 4, 2, 11, 12, 4, 13, 7, 2, 14, 2, 15, 8, 4, 16, 17, 2, 4, 8, 5, 2, 18, 2, 7, 19, 4, 2, 20, 21, 22, 8, 7, 2, 23, 24, 25, 8, 4, 2, 26, 2, 4, 27, 28, 29, 30, 2, 7, 8, 31, 2, 32, 2, 4, 33, 7, 34, 30, 2, 9, 35, 4, 2, 36, 37, 4, 8, 25, 2, 38, 39, 7, 8, 4, 40

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OFFSET

1,2

COMMENTS

Restricted growth sequence transform of the ordered pair [A003557(n), A329345(n)].

LINKS

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

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; };

A003557(n) = (n/factorback(factorint(n)[, 1]));

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]) };

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

A324886(n) = A276086(A108951(n));

A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};

A329044(n) = A064989(A324886(n));

A246277(n) = if(1==n, 0, my(f = factor(n), k = primepi(f[1, 1])-1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-k)); factorback(f)/2);

v351949 = rgs_transform(vector(up_to, n, [A003557(n), A246277(A329044(n))]));

A351949(n) = v351949[n];

CROSSREFS

Cf. A003557, A305800, A329044, A329345, A329620.