A373595 -id:A373595 - cp's OEIS frontend

A373593 Lexicographically earliest infinite sequence such that for all i, j >= 1, a(i) = a(j) => f(i) = f(j), where f(n<=3) = n, f(p) = 0 for primes p > 3, and for composite n, f(n) = [A007949(n), A046523(A248909(n)), A046523(A343430(n))].

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

Offset: 1

Antti Karttunen, Jun 13 2024

nonn

Restricted growth sequence transform of the function f given in the definition.
For all i, j >= 1:
  a(i) = a(j) => A373595(i) = A373595(j),
  a(i) = a(j) => A353815(i) = A353815(j),
  a(i) = a(j) => A353816(i) = A353816(j).

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

Cf. A007949, A046523, A248909, A343430.

Cf. A353815, A353816, A373595.

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; };
A007949(n) = valuation(n,3);
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
A248909(n) = { my(f=factor(n)); for(k=1, #f~, if(1!=(f[k,1]%3), f[k,1]=1)); factorback(f); };
A343430(n) = { my(f=factor(n)); for(k=1, #f~, if(2!=(f[k,1]%3), f[k,1]=1)); factorback(f); };
Aux373593(n) = if(n<3, n, [A007949(n), A046523(A248909(n)), A046523(A343430(n))]);
v373593 = rgs_transform(vector(up_to, n, Aux373593(n)));
A373593(n) = v373593[n];

A373594 Lexicographically earliest infinite sequence such that for all i, j >= 1, a(i) = a(j) => f(i) = f(j), where f(n<=3) = n, f(p) = 0 for primes p > 3, and for composite n, f(n) = [A007814(n), A065339(n), A083025(n), A373591(n), A373592(n)].

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jun 13 2024

nonn

Restricted growth sequence transform of the function f given in the definition.
Note that for composite n, f(n) can be defined in general as a quintuple vector [v(n), w(n), x(n), y(n), z(n)], where v, w, x, y and z are any five of these six sequences: A007814, A007949, A065339, A083025, A373591, A373592. This follows because A007814(n) + A065339(n) + A083025(n) = A007949(n) + A373591(n) + A373592(n) = A001222(n), so the omitted sixth element can be always worked out from the remaining five.
For all i, j > 1:
  A305900(i) = A305900(j) => a(i) = a(j) => A373595(i) = A373595(j).

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

Cf. A007814, A007949, A065339, A083025, A373591, A373592.

Cf. also A305900, A373595.

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; };
A007814(n) = valuation(n,2);
A065339(n) = sum(i=1, #n=factor(n)~, (3==n[1, i]%4)*n[2, i]);
A083025(n) = sum(i=1, #n=factor(n)~, (1==n[1, i]%4)*n[2, i]);
A373591(n) = sum(i=1, #n=factor(n)~, (1==n[1, i]%3)*n[2, i]);
A373592(n) = sum(i=1, #n=factor(n)~, (2==n[1, i]%3)*n[2, i]);
Aux373594(n) = if(n<=3, n, if(isprime(n), 0, [A007814(n), A083025(n), A065339(n), A373591(n), A373592(n)]));
v373594 = rgs_transform(vector(up_to, n, Aux373594(n)));
A373594(n) = v373594[n];

cp's OEIS Frontend

A373593 Lexicographically earliest infinite sequence such that for all i, j >= 1, a(i) = a(j) => f(i) = f(j), where f(n<=3) = n, f(p) = 0 for primes p > 3, and for composite n, f(n) = [A007949(n), A046523(A248909(n)), A046523(A343430(n))].

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