A347385 -id:A347385 - cp's OEIS frontend

A347387 The exponent of the first power of 2 reached when starting iterating A347385 from n, where A347385 is Dedekind psi function applied to the odd part of n.

0, 1, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 3, 3, 2, 4, 2, 2, 2, 2, 5, 2, 2, 2, 2, 3, 2, 3, 2, 2, 5, 5, 2, 2, 2, 2, 2, 2, 3, 2, 5, 5, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 5, 5, 2, 6, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 5, 5, 5, 2, 2, 2, 2, 2, 2, 3, 2, 7, 2, 2, 2, 3, 3, 2, 2, 2, 2, 3, 3, 2

Offset: 1

Antti Karttunen, Aug 31 2021

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000265, A001615, A007814, A209229, A347385, A347386.

Cf. also A049113, A347388.

f[p_, e_] := If[p == 2, 1, (p + 1)*p^(e - 1)]; psiOdd[1] = 1; psiOdd[n_] := Times @@ f @@@ FactorInteger[n]; a[n_] := IntegerExponent[NestWhile[psiOdd, n, # != 2^IntegerExponent[#, 2] &], 2]; Array[a, 100] (* Amiram Eldar, Aug 31 2021 *)

A347385(n) = if(1==n,n, my(f=factor(n>>valuation(n, 2))); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1)));
A347387(n) = if(!bitand(n, n-1), valuation(n, 2), A347387(A347385(n)));

a(2^k) = k, and for numbers with A209229(n) = 0, a(n) = a(A001615(A000265(n))).

A351035 Lexicographically earliest infinite sequence such that a(i) = a(j) => A347385(i) = A347385(j) and A336158(i) = A336158(j), for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jan 30 2022

Restricted growth sequence transform of the ordered pair [A347385(n), A336158(n)], where A347385(n) is the Dedekind psi function applied to the odd part of n, i.e., A001615(A000265(n)), and A336158(n) is the least representative of the prime signature of the odd part of n.

For all i, j >= 1: A003602(i) = A003602(j) => a(i) = a(j).

			a(33) = a(35) as both 33 = 3*11 and 35 = 5*7 are odd nonsquare semiprimes, thus A336158 gives equal values for them, and also A347385(33) = A001615(33) = A347385(35) = A001615(35) = 48.

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000265, A001615, A003602, A046523, A336158, A351035.
Differs from A347374 for the first time at n=103, where a(103) = 48, while A347374(103) = 30.
Differs from A351036 for the first time at n=175, where a(175) = 78, while A351036(175) = 80.

up_to = 65537;
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; };
A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A336158(n) = A046523(A000265(n));
A347385(n) = if(1==n,n, my(f=factor(n>>valuation(n, 2))); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1)));
Aux351035(n) = [A347385(n), A336158(n)];
v351035 = rgs_transform(vector(up_to, n, Aux351035(n)));
A351035(n) = v351035[n];

A347386 Number of iterations of A347385 (Dedekind psi function applied to the odd part of n) needed to reach a power of 2.

Original entry on oeis.org

0, 0, 1, 0, 2, 1, 1, 0, 2, 2, 2, 1, 2, 1, 2, 0, 3, 2, 3, 2, 1, 2, 2, 1, 3, 2, 3, 1, 3, 2, 1, 0, 2, 3, 2, 2, 4, 3, 2, 2, 2, 1, 3, 2, 3, 2, 2, 1, 2, 3, 3, 2, 4, 3, 3, 1, 3, 3, 3, 2, 2, 1, 2, 0, 2, 2, 4, 3, 2, 2, 3, 2, 5, 4, 3, 3, 2, 2, 3, 2, 4, 2, 2, 1, 4, 3, 3, 2, 4, 3, 2, 2, 1, 2, 3, 1, 3, 2, 3, 3, 4, 3, 3, 2, 2

Offset: 1

Antti Karttunen, Aug 31 2021

nonn

Also, for n > 1, one less than the number of iterations of A347385 to reach 1.

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A000265, A001615, A209229, A347385, A347387 (the exponent of the eventual power of 2 reached).

Cf. also A003434, A019269, A227944, A256757, A331410, A336361 for similar sequences.

f[p_, e_] := If[p == 2, 1, (p + 1)*p^(e - 1)]; psiOdd[1] = 1; psiOdd[n_] := Times @@ f @@@ FactorInteger[n]; a[n_] := -1 + Length @ NestWhileList[psiOdd, n, # != 2^IntegerExponent[#, 2] &]; Array[a, 100] (* Amiram Eldar, Aug 31 2021 *)

A347385(n) = if(1==n,n, my(f=factor(n>>valuation(n, 2))); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1)));
A347386(n) = if(!bitand(n, n-1), 0, 1+A347386(A347385(n)));

If A209229(n) = 1, then a(n) = 0, otherwise a(n) = 1 + a(A001615(A000265(n))).

For all n >= 1, a(n) <= A331410(n).

A366885 Dedekind psi function applied to the odd part of n, permuted by A163511: a(n) = A347385(A163511(n)).

Original entry on oeis.org

1, 1, 1, 4, 1, 12, 4, 6, 1, 36, 12, 30, 4, 24, 6, 8, 1, 108, 36, 150, 12, 120, 30, 56, 4, 72, 24, 48, 6, 32, 8, 12, 1, 324, 108, 750, 36, 600, 150, 392, 12, 360, 120, 336, 30, 224, 56, 132, 4, 216, 72, 240, 24, 192, 48, 96, 6, 96, 32, 72, 8, 48, 12, 14, 1, 972, 324, 3750, 108, 3000, 750, 2744, 36, 1800, 600, 2352

Offset: 0

Antti Karttunen, Nov 04 2023

nonn

Antti Karttunen, Table of n, a(n) for n = 0..16384

Cf. A001615, A163511, A347385, A366886 (rgs-transform).

Cf. also A324186.

A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A347385(n) = if(1==n,n, my(f=factor(n>>valuation(n, 2))); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1)));
A366885(n) = A347385(A163511(n));

A351461 Lexicographically earliest infinite sequence such that a(i) = a(j) => A206787(i) = A206787(j) and A336651(i) = A336651(j) for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Feb 11 2022

nonn

Restricted growth sequence transform of the ordered pair [A206787(n), A336651(n)], or equally, of sequence b(n) = A291750(A000265(n)).
For all i, j >= 1:
  A003602(i) = A003602(j) => A351040(i) = A351040(j) => a(i) = a(j),
  A324400(i) = A324400(j) => A351460(i) = A351460(j) => a(i) = a(j),
  a(i) = a(j) => A000593(i) = A000593(j),
  a(i) = a(j) => A347385(i) = A347385(j),
  a(i) = a(j) => A351037(i) = A351037(j) => A347240(i) = A347240(j).
From Antti Karttunen, Nov 23 2023: (Start)
Conjectured to be equal to the lexicographically earliest infinite sequence such that b(i) = b(j) => A000593(i) = A000593(j) and A336467(i) = A336467(j) for all i, j >= 1. In any case, a(i) = a(j) => b(i) = b(j) for all i, j >= 1 [because both A000593(n) and A336467(n) can be computed from the values of A206787(n) and A336651(n)], but whether the implication holds to the opposite direction is still open. Empirically this has been checked up to n = 2^22. See also comment in A351040.
(End)

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A206787, A336651.
Cf. also A000593, A003602, A291750, A291751, A324400, A336467, A347240, A347385, A351040, A351460.
Differs from A351037 for the first time at n=103, where a(103) = 42 while A351037(103) = 27.

up_to = 65537;
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; };
A206787(n) = sumdiv(n, d, d*(d % 2)*issquarefree(d)); \\ From A206787
A336651(n) = { my(f=factor(n)); prod(i=1, #f~, if(2==f[i,1],1,f[i,1]^(f[i,2]-1))); };
Aux351461(n) = [A206787(n), A336651(n)];
v351461 = rgs_transform(vector(up_to, n, Aux351461(n)));
A351461(n) = v351461[n];

A366881 Lexicographically earliest infinite sequence such that a(i) = a(j) => A206787(A163511(i)) = A206787(A163511(j)) and A336651(A163511(n)) = A336651(A163511(j)) for all i, j >= 0.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Nov 04 2023

nonn

Restricted growth sequence transform of the ordered pair [A206787(A163511(n)), A336651(A163511(n))].
Restricted growth sequence transform of sequence b(n) = A351461(A163511(n)).
For all i, j >= 0:
  a(i) = a(j) => A324186(i) = A324186(j), (similarly for A366806)
  a(i) = a(j) => A366885(i) = A366885(j). (similarly for A366886).

Antti Karttunen, Table of n, a(n) for n = 0..65537

Cf. A000265, A000593, A163511, A347385, A351461, A366887.
Cf. also A324186, A366806, A366885, A366886, A366888.
Differs from A366806 for the first time at n=105, where a(105) = 52, while A366806(105) = 19.

up_to = 65537;
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; };
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A206787(n) = sumdiv(n, d, d*issquarefree(2*d));
A336651(n) = { my(f=factor(n>>valuation(n,2))); prod(i=1, #f~, f[i,1]^(f[i,2]-1)); };
A366881aux(n) = [A206787(A163511(n)), A336651(A163511(n))];
v366881 = rgs_transform(vector(1+up_to,n,A366881aux(n-1)));
A366881(n) = v366881[1+n];

For all n >= 1, a(n) = a(2*n) = a(A000265(n)).

A366886 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366885(i) = A366885(j) for all i, j >= 0.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Nov 04 2023

Restricted growth sequence transform of A366885.

Albeit quite ugly, the scatter plot is still interesting. - Antti Karttunen, Jan 03 2024

Antti Karttunen, Table of n, a(n) for n = 0..65537

Cf. A163511, A347385, A366885.

Cf. also A366806, A366881, A366891 (compare the scatter plots).

up_to = 65537;
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; };
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A347385(n) = if(1==n,n, my(f=factor(n>>valuation(n, 2))); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1)));
A366885(n) = A347385(A163511(n));
v366886 = rgs_transform(vector(1+up_to,n,A366885(n-1)));
A366886(n) = v366886[1+n];

A366891 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j), A206787(A163511(i)) = A206787(A163511(j)) and A336651(A163511(n)) = A336651(A163511(j)) for all i, j >= 0.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Nov 04 2023

nonn

Restricted growth sequence transform of the triplet [A365425(n), A206787(A163511(n)), A336651(A163511(n))], and also by conjecture, of sequence b(n) = A351040(A163511(n)).
For all i, j >= 0:
  a(i) = a(j) => A365395(i) = A365395(j),
  a(i) = a(j) => A366874(i) = A366874(j),
  a(i) = a(j) => A366881(i) = A366881(j).

Antti Karttunen, Table of n, a(n) for n = 0..65537

Cf. A000265, A000593, A163511, A347385, A351040, A351461, A365425.
Differs from A366806 for the first time at n=105, where a(105) = 52, while A366806(105) = 19.
Differs from A366881 for the first time at n=511, where a(511) = 249, while A366881(511) = 7.

up_to = 65537;
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; };
A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A365425(n) = A046523(A000265(A163511(n)));
A206787(n) = sumdiv(n, d, d*issquarefree(2*d));
A336651(n) = { my(f=factor(n>>valuation(n,2))); prod(i=1, #f~, f[i,1]^(f[i,2]-1)); };
A366891aux(n) = [A365425(n), A206787(A163511(n)), A336651(A163511(n))];
v366891 = rgs_transform(vector(1+up_to,n,A366891aux(n-1)));
A366891(n) = v366891[1+n];

For all n >= 1, a(n) = a(2*n) = a(A000265(n)).

A347288 Irregular triangle T(n,k) starting with 2^n followed by p_k^e_k = p_k^floor(log_p_k(p_(k-1)^e_(k-1))) such that e_k > 0.

Original entry on oeis.org

1, 2, 4, 3, 8, 3, 16, 9, 5, 32, 27, 25, 7, 64, 27, 25, 7, 128, 81, 25, 7, 256, 243, 125, 49, 11, 512, 243, 125, 49, 11, 1024, 729, 625, 343, 121, 13, 2048, 729, 625, 343, 121, 13, 4096, 2187, 625, 343, 121, 13, 8192, 6561, 3125, 2401, 1331, 169, 17

Offset: 0

Michael De Vlieger, Aug 28 2021

T(0,1) = 1 by convention.

T(n,1) = 2^n. T(n,k) = p_k^e_k such that p_k^T(n,k) is the largest 1 < p_k^e_k < p_(k-1)^e_(k-1).

			Row 0 contains {1} by convention.
Row 1 contains {2} since no nonzero exponent e exists such that 3^e < 2^1.
Row 2 contains {4,3} since 3^1 < 2^2 yet 3^2 > 2^2. (We assume hereinafter that the powers listed are the largest possible smaller than the immediately previous term.)
Row 3 contains {8,3} since 2^3 > 3^1.
Row 4 contains {16,9,5} since 2^4 > 3^2 > 5^1, etc.
Triangle begins:
           2      3      5      7     11    13    17  ...
  --------------------------------------------------
  0:       1
  1:       2
  2:       4      3
  3:       8      3
  4:      16      9      5
  5:      32     27     25      7
  6:      64     27     25      7
  7:     128     81     25      7
  8:     256    243    125     49     11
  9:     512    243    125     49     11
  10:   1024    729    625    343    121    13
  11:   2048    729    625    343    121    13
  12:   4096   2187    625    343    121    13
  13:   8192   6561   3125   2401   1331   169   17
  14:  16384   6561   3125   2401   1331   169   17
  ...

Michael De Vlieger, Table of n, a(n) for n = 0..10367 (rows 0 <= n <= 300, flattened)

Cf. A000217, A000961, A089576, A347284.

{{1}}~Join~Array[Most@ NestWhile[Block[{p = Prime[#2]}, Append[#1, p^Floor@ Log[p, #1[[-1]]]]] & @@ {#, Length@ # + 1} &, {2^#}, #[[-1]] > 1 &] &, 13] (* Michael De Vlieger, Aug 28 2021 *)

T(n,1) = 2^n; T(n,k) = p_k^floor(log_p_k(p_(k-1)^T(n,k-1))).
A347385(n,k) = p_k^T(n,k).
A089576(n) = row lengths.
A347284(n) = product of row n.

A351455 a(n) = A064989(A001615(A003961(n))).

Original entry on oeis.org

1, 1, 2, 2, 1, 2, 2, 4, 6, 1, 5, 4, 4, 2, 2, 8, 3, 6, 2, 2, 4, 5, 6, 8, 5, 4, 18, 4, 1, 2, 17, 16, 10, 3, 2, 12, 10, 2, 8, 4, 7, 4, 2, 10, 6, 6, 8, 16, 14, 5, 6, 8, 6, 18, 5, 8, 4, 1, 29, 4, 13, 17, 12, 32, 4, 10, 4, 6, 12, 2, 31, 24, 3, 10, 10, 4, 10, 8, 10, 8, 54, 7, 12, 8, 3, 2, 2, 20, 25, 6, 8

Offset: 1

Antti Karttunen, Feb 12 2022

Antti Karttunen, Table of n, a(n) for n = 1..20000
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences computed from indices in prime factorization

Cf. A001615, A003557, A003961, A064989, A151800, A347385, A351450.
Coincides with A326042 on squarefree numbers (A005117, and apparently on no other numbers).
Cf. also A351441.

A001615(n) = if(1==n,n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A064989(n) = { my(f = factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
A351455(n) = A064989(A001615(A003961(n)));

Multiplicative with a(p^e) = A064989((q+1)*q^(e-1)), where q = nextPrime(p) = A151800(p).
a(n) = A064989(A001615(A003961(n))) = A064989(A347385(A003961(n))).
a(n) = A003557(n) * A351450(n).

cp's OEIS Frontend

A347387 The exponent of the first power of 2 reached when starting iterating A347385 from n, where A347385 is Dedekind psi function applied to the odd part of n.

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A351035 Lexicographically earliest infinite sequence such that a(i) = a(j) => A347385(i) = A347385(j) and A336158(i) = A336158(j), for all i, j >= 1.

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PARI

A347386 Number of iterations of A347385 (Dedekind psi function applied to the odd part of n) needed to reach a power of 2.

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Mathematica

PARI

Formula

A366885 Dedekind psi function applied to the odd part of n, permuted by A163511: a(n) = A347385(A163511(n)).

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PARI

A351461 Lexicographically earliest infinite sequence such that a(i) = a(j) => A206787(i) = A206787(j) and A336651(i) = A336651(j) for all i, j >= 1.

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PARI

A366881 Lexicographically earliest infinite sequence such that a(i) = a(j) => A206787(A163511(i)) = A206787(A163511(j)) and A336651(A163511(n)) = A336651(A163511(j)) for all i, j >= 0.

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PARI

Formula

A366886 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366885(i) = A366885(j) for all i, j >= 0.

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PARI

A366891 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j), A206787(A163511(i)) = A206787(A163511(j)) and A336651(A163511(n)) = A336651(A163511(j)) for all i, j >= 0.

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PARI

Formula

A347288 Irregular triangle T(n,k) starting with 2^n followed by p_k^e_k = p_k^floor(log_p_k(p_(k-1)^e_(k-1))) such that e_k > 0.

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