A369445 -id:A369445 - cp's OEIS frontend

A369261 Lexicographically earliest infinite sequence such that a(i) = a(j) => A324644(i) = A324644(j) and A369445(i) = A369445(j), for all i, j >= 1.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 15, 23, 16, 20, 24, 25, 26, 27, 21, 28, 29, 30, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 29, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 35, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 62, 53, 51, 70, 71, 72, 58, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 63

Offset: 1

Antti Karttunen, Jan 25 2024

nonn

Restricted growth sequence transform of the ordered pair [A324644(n), A369445(n)], or equally, of the pair [A000203(n), A324644(n)], or equally, of the pair [A000203(n), A369445(n)].

For all i, j >= 1: a(i) = a(j) => A286603(i) = A286603(j).

Cf. A000203, A276086, A324644, A369445.

Cf. also A286603, A291751, A369260 and A353523, A369047, A369051, A369062.

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; };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A324644(n) = gcd(sigma(n),A276086(n));
Aux369261(n) = { my(u=A324644(n)); [u, sigma(n)/u]; };
v369261 = rgs_transform(vector(up_to, n, Aux369261(n)));
A369261(n) = v369261[n];

A369446 Denominator of sigma(n) / A276086(n), where A276086 is the primorial base exp-function.

Original entry on oeis.org

2, 1, 3, 9, 3, 5, 5, 1, 30, 5, 15, 25, 25, 25, 25, 225, 25, 125, 25, 125, 375, 125, 375, 125, 1250, 625, 375, 5625, 375, 7, 7, 1, 7, 7, 21, 5, 35, 7, 15, 7, 15, 175, 175, 25, 175, 175, 525, 875, 1750, 875, 875, 1125, 875, 875, 4375, 875, 2625, 875, 2625, 7, 49, 49, 147, 441, 21, 245, 245, 35, 245, 245, 245, 245, 1225

Offset: 1

Antti Karttunen, Jan 25 2024

Cf. A000203, A276086, A324644, A369445 (numerators).

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A369446(n) = { my(u=A276086(n)); (u/gcd(u,sigma(n))); };

a(n) = A276086(n) / A324644(n).

cp's OEIS Frontend

A369261 Lexicographically earliest infinite sequence such that a(i) = a(j) => A324644(i) = A324644(j) and A369445(i) = A369445(j), for all i, j >= 1.

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