A373250 -id:A373250 - cp's OEIS frontend

A373251 Lexicographically earliest infinite sequence such that a(i) = a(j) => A181819(i) = A181819(j), i mod A181819(i) = j mod A181819(j), and gcd(i,A276086(i)) = gcd(j,A276086(j)), for all i, j >= 1, where A181819 is the prime shadow of n, and A276086 is the primorial base exp-function.

1, 2, 3, 4, 5, 6, 5, 7, 8, 9, 5, 10, 5, 6, 11, 12, 5, 10, 5, 13, 14, 6, 5, 15, 16, 6, 17, 18, 5, 19, 5, 20, 14, 6, 21, 22, 5, 6, 23, 24, 5, 25, 5, 26, 27, 6, 5, 28, 29, 30, 23, 18, 5, 15, 31, 32, 14, 6, 5, 33, 5, 6, 34, 35, 36, 37, 5, 26, 14, 38, 5, 39, 5, 6, 40, 18, 41, 19, 5, 42, 43, 6, 5, 44, 45, 6, 23, 46, 5, 47, 21, 26, 14, 6

Offset: 1

Antti Karttunen, May 30 2024

nonn

Restricted growth sequence transform of the triple [A181819(n), A373247(n), A324198(n)].
For all i, j:
  A305900(i) = A305900(j) => a(i) = a(j),
  a(i) = a(j) => A373248(i) = A373248(j),
  a(i) = a(j) => A373250(i) = A373250(j).

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A101296, A181819, A324198, A373247, A373248, A373250.

up_to = 100000;
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; };
A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
A324198(n) = { my(m=1, p=2, orgn=n); while(n, m *= (p^min(n%p, valuation(orgn, p))); n = n\p; p = nextprime(1+p)); (m); };
Aux373251(n) = [A181819(n), n%A181819(n), A324198(n)];
v373251 = rgs_transform(vector(up_to, n, Aux373251(n)));
A373251(n) = v373251[n];

A373980 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A003415(n), A085731(n), A181819(n), A373247(n)], for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jun 24 2024

nonn

Restricted growth sequence transform of the quadruple [A003415(n), A085731(n), A181819(n), A373247(n)].
For all i, j >= 1:
  A305801(i) = A305801(j) => a(i) = a(j),
  a(i) = a(j) => A300249(i) = A300249(j) => A101296(i) = A101296(j),
  a(i) = a(j) => A369051(i) = A369051(j),
  a(i) = a(j) => A373250(i) = A373250(j).

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A003415, A085731, A181819, A373247.
Cf. A101296, A300249, A305801, A369051, A373250.
Differs from A353520 and A361021 first at n=130, where a(130) = 82, while A353520(130) = A361021(130) = 96.

up_to = 100000;
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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
Aux373980(n) = { my(d=A003415(n), s=A181819(n)); [d, s, gcd(n,d), n%s]; };
v373980 = rgs_transform(vector(up_to, n, Aux373980(n)));
A373980(n) = v373980[n];

A373981 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A107463(n), A181819(n), A373247(n)], for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jun 24 2024

nonn

Restricted growth sequence transform of the triple [A107463(n), A181819(n), A373247(n)].
For all i, j >= 1:
  A305801(i) = A305801(j) => a(i) = a(j),
  a(i) = a(j) => A373250(i) = A373250(j) => A101296(i) = A101296(j),
  a(i) = a(j) => A373976(i) = A373976(j).

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A107463, A181819, A373247.
Cf. A101296, A305801, A373250, A373976.
Cf. also A373379, A373980.

up_to = 100000;
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; };
A001414(n) = ((n=factor(n))[, 1]~*n[, 2]);
A107463(n) = if(n<=1,n,if(isprime(n),1,A001414(n)));
A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
Aux373981(n) = { my(s=A181819(n)); [A107463(n), s, n%s]; };
v373981 = rgs_transform(vector(up_to, n, Aux373981(n)));
A373981(n) = v373981[n];

cp's OEIS Frontend

A373251 Lexicographically earliest infinite sequence such that a(i) = a(j) => A181819(i) = A181819(j), i mod A181819(i) = j mod A181819(j), and gcd(i,A276086(i)) = gcd(j,A276086(j)), for all i, j >= 1, where A181819 is the prime shadow of n, and A276086 is the primorial base exp-function.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A373980 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A003415(n), A085731(n), A181819(n), A373247(n)], for all i, j >= 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A373981 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A107463(n), A181819(n), A373247(n)], for all i, j >= 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI