A373983 Lexicographically earliest infinite sequence such that a(i) = a(j) = A246277(A324886(i)) = A246277(A324886(j)) and A278226(A328768(i)) = A278226(A328768(j)), for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, Jun 25 2024

Keywords

• nonn
• look

Comments

Restricted growth sequence transform of the ordered pair [A246277(A276086(A108951(n))), A046523(A276086(A328768(n)))].

For all i, j >= 1:

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

a(i) = a(j) => A329345(i) = A329345(j) => A329045(i) = A329045(j),

a(i) = a(j) => A373982(i) = A373982(j) => A328771(i) = A328771(j).

It is hard to say for sure which graphical features in the scatter plot have their provenance in A373982, and which ones in A329345.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A002110, A046523, A108951, A246277, A276086, A278226, A324886, A328768.

Cf. A305800, A329045, A329345, A328771, A373982.

Cf. also A329620.

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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
A108951(n) = { my(f=factor(n)); prod(i=1, #f~,  prod(i=1, primepi(f[i, 1]), prime(i))^f[i, 2]); };
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);
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A002110(n) = prod(i=1,n,prime(i));
A328768(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*A002110(primepi(f[i,1])-1)/f[i, 1]));
Aux373983(n) = [A246277(A276086(A108951(n))), A046523(A276086(A328768(n)))];
v373983 = rgs_transform(vector(up_to, n, Aux373983(n)));
A373983(n) = v373983[n];