A336926 -id:A336926 - cp's OEIS frontend

A336927 Lexicographically earliest infinite sequence such that a(i) = a(j) => A335880(sigma(i)) = A335880(sigma(j)), for all i, j >= 1.

1, 2, 1, 3, 2, 2, 1, 4, 5, 5, 2, 3, 3, 2, 2, 6, 5, 7, 8, 9, 1, 5, 2, 4, 6, 9, 8, 3, 4, 5, 1, 10, 2, 7, 2, 10, 7, 4, 3, 11, 9, 2, 5, 9, 7, 5, 2, 6, 12, 13, 5, 13, 7, 4, 5, 4, 8, 11, 4, 9, 6, 2, 5, 14, 9, 5, 15, 10, 2, 5, 5, 16, 11, 12, 6, 7, 2, 9, 8, 13, 12, 10, 9, 3, 7, 7, 4, 11, 11, 12, 3, 9, 1, 5, 4, 10, 13, 17, 7, 18, 19, 7, 5, 12, 2

Offset: 1

Antti Karttunen, Aug 11 2020

nonn

Restricted growth sequence transform of the function f(n) = A335880(A000203(n)), or equally, of the ordered pair [A336928(n), A336929(n)].

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

Cf. A000203, A335880, A336928, A336929.

Cf. also A336926.

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; };
A329697(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A329697(f[k,1]-1)))); };
A331410(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A331410(f[k,1]+1)))); };
Aux335880(n) = [A329697(n),A331410(n)];
v336927 = rgs_transform(vector(up_to, n, Aux335880(sigma(n))));
A336927(n) = v336927[n];

A336925 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336147(1+sigma(i)) = A336147(1+sigma(j)), for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Aug 10 2020

nonn

Restricted growth sequence transform of the function f(n) = A336147(A088580(n)).
For all i, j:
  A324400(i) = A324400(j) => a(i) = a(j),
  a(i) = a(j) => A336691(i) = A336691(j),
  a(i) = a(j) => A336924(i) = A336924(j).

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

Cf. also A336926.

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; };
A020639(n) = if(1==n, n, factor(n)[1, 1]);
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A122111(n) = if(1==n,n,my(f=factor(n), es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
A278221(n) = A046523(A122111(n));
Aux336147(n) = [A020639(n),A278221(n)];
v336925 = rgs_transform(vector(up_to, n, Aux336147(1+sigma(n))));
A336925(n) = v336925[n];

cp's OEIS Frontend

A336927 Lexicographically earliest infinite sequence such that a(i) = a(j) => A335880(sigma(i)) = A335880(sigma(j)), for all i, j >= 1.

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