A318831 -id:A318831 - cp's OEIS frontend

A318835 Restricted growth sequence transform of A318834, product_{d|n, dA019565(A000010(d)).

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

Offset: 1

Antti Karttunen, Sep 04 2018

nonn

For all i, j: a(i) = a(j) => A051953(i) = A051953(j).

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

Cf. A000010, A019565, A318831, A318834,

Cf. also A293215, A293217, A293223, A293224, A293232, A300833, A300835.

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; };
A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
A318834(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A019565(eulerphi(d)))); m; };
v318835 = rgs_transform(vector(up_to,n,A318834(n)));
A318835(n) = v318835[n];

A318832 Restricted growth sequence transform of A278222(A000203(n)).

Original entry on oeis.org

1, 2, 1, 3, 2, 2, 1, 4, 5, 6, 2, 3, 3, 2, 2, 7, 6, 8, 6, 9, 1, 6, 2, 4, 7, 9, 6, 3, 4, 6, 1, 10, 2, 11, 2, 12, 5, 4, 3, 13, 9, 2, 5, 9, 8, 6, 2, 7, 8, 14, 6, 5, 11, 4, 6, 4, 6, 13, 4, 9, 7, 2, 5, 15, 9, 6, 6, 10, 2, 6, 6, 11, 9, 8, 7, 5, 2, 9, 6, 14, 16, 10, 9, 3, 11, 6, 4, 13, 13, 14, 3, 9, 1, 6, 4, 10, 5, 17, 8, 12, 11, 11, 5, 13, 2

Offset: 1

Antti Karttunen, Sep 04 2018

nonn

Sequence allots a distinct value for each distinct multiset formed from the lengths of 1-runs in the binary representation of A000203(n).

For all i, j: a(i) = a(j) => A175548(i) = A175548(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to sigma(n)

Cf. A000203, A278222.

Cf. also A286622, A304101, A318831.

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; };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A278222(n) = A046523(A005940(1+n));
v318832 = rgs_transform(vector(up_to,n,A278222(sigma(n))));
A318832(n) = v318832[n];

cp's OEIS Frontend

A318835 Restricted growth sequence transform of A318834, product_{d|n, dA019565(A000010(d)).

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