A374033 -id:A374033

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A374032

Lexicographically earliest infinite sequence such that a(i) = a(j) => A278226(A374031(i)) = A278226(A374031(j)), for all i, j >= 1.

+10
2

1, 2, 2, 2, 2, 2, 2, 3, 4, 2, 2, 4, 2, 2, 4, 4, 2, 2, 2, 4, 3, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 5, 4, 2, 4, 2, 2, 2, 4, 6, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 4, 4, 2, 2, 3, 3, 7, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2, 4, 8, 2, 2, 2, 3, 2, 2, 2, 4, 2, 4, 3, 2, 2, 9, 4, 3, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 3, 6

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OFFSET

1,2

COMMENTS

Restricted growth sequence transform of A278226(A374031(n)).

For all i, j >= 1:

A305800(i) = A305800(j) => a(i) = a(j) => A374034(i) = A374034(j).

LINKS

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

Index entries for sequences related to primorial numbers

PROG

(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; };

A002110(n) = prod(i=1, n, prime(i));

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };

A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };

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

A278226(n) = A046523(A276086(n));

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]));

A374031(n) = gcd(A276085(n), A328768(n));

v374032 = rgs_transform(vector(up_to, n, A278226(A374031(n))));

A374032(n) = v374032[n];

CROSSREFS

Cf. A002110, A046523, A276085, A276086, A278226, A328768, A374031.

Cf. A305800, A374034.

Cf. also A373982, A374033.

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 27 2024

STATUS

approved

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