A329353 -id:A329353 - cp's OEIS frontend

A329351 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329350(i) = A329350(j) for all i, j.

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

Offset: 1

Antti Karttunen, Nov 12 2019

nonn

Restricted growth sequence transform of A329350.
For all i, j:
  A305800(i) = A305800(j) => a(i) = a(j),
  a(i) = a(j) => A069359(i) = A069359(j).

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

Cf. A069359, A305800, A329350.

Cf. also A329353, A329381.

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); };
A329350(n) = { my(m=1); fordiv(n,d,if(isprime(n/d), m *= A276086(d))); (m); };
v329351 = rgs_transform(vector(up_to, n, A329350(n)));
A329351(n) = v329351[n];

A329352 a(n) = Product_{d|n} A019565(d)^A010051(n/d).

Original entry on oeis.org

1, 2, 2, 3, 2, 18, 2, 5, 6, 30, 2, 75, 2, 90, 60, 7, 2, 210, 2, 105, 180, 126, 2, 245, 10, 210, 14, 525, 2, 66150, 2, 11, 252, 66, 300, 1155, 2, 198, 420, 385, 2, 173250, 2, 825, 2940, 990, 2, 847, 30, 3234, 132, 1155, 2, 15246, 420, 2695, 396, 2310, 2, 2223375, 2, 6930, 1540, 13, 700, 64350, 2, 195, 1980, 171990, 2, 5005, 2, 390, 32340, 975, 1260

Offset: 1

Antti Karttunen, Nov 12 2019

nonn

			The divisors of 30 are [1, 2, 3, 5, 6, 10, 15, 30], of which only d = 6, 10 and 15 are such that 30/d is a prime, thus a(n) = A019565(6) * A019565(10) * A019565(15) = 15 * 21 * 210 = 66150.

Antti Karttunen, Table of n, a(n) for n = 1..8192

Cf. A010051, A019565, A048675, A069359, A329353 (rgs-transform).
Cf. also A329350.
Differs from A300832 for the first time at n=30, where a(30) = 66150, while A300832(30) = 132300.

A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
A329352(n) = { my(m=1); fordiv(n,d,if(isprime(n/d), m *= A019565(d))); (m); };

a(n) = Product_{d|n} A019565(d)^A010051(n/d).

For all n, A048675(a(n)) = A069359(n).

cp's OEIS Frontend

A329351 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329350(i) = A329350(j) for all i, j.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI