A353560 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j), A001065(i) = A001065(j) and A051953(i) = A051953(j), for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, Apr 29 2022

Keywords

• nonn

Comments

Restricted growth sequence transform of the triplet [A046523(n), A001065(n), A051953(n)].

For all i,j:

A305800(i) = A305800(j) => a(i) = a(j),

a(i) = a(j) => A300232(i) = A300232(j), [Combining A046523 and A051953]

a(i) = a(j) => A300235(i) = A300235(j), [Combining A046523 and A001065]

a(i) = a(j) => A305895(i) = A305895(j), [Combining A001065 and A051953]

a(i) = a(j) => A353276(i) = A353276(j). [Needs all three components]

Links

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

Crossrefs

Cf. A001065, A046523, A051953.

Cf. also A101296, A305800, A300232, A353276.

Differs from A300235 for the first time at n=153, where a(153) = 110, while A300235(153) = 106.

Differs from A305895 for the first time at n=3283, where a(3283) = 2502, while A305895(3283) = 1845.

Differs from A327931 for the first time at n=4433, where a(4433) = 2950, while A327931(4433) = 3393.

Differs from A300249 and from A351260 for the first time at n=105, where a(105) = 75, while A300249(105) = A351260(105) = 56.

Programs

PARI

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; };
A001065(n) = (sigma(n)-n);
A051953(n) = (n-eulerphi(n));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
Aux353560(n) = [A046523(n), A001065(n), A051953(n)];
v353560 = rgs_transform(vector(up_to,n,Aux353560(n)));
A353560(n) = v353560[n];