A336926 - OEIS

A336926

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

1, 1, 2, 1, 3, 4, 4, 1, 3, 5, 4, 6, 7, 8, 8, 1, 5, 2, 9, 10, 5, 6, 8, 9, 1, 10, 7, 11, 12, 13, 5, 1, 14, 6, 14, 9, 5, 9, 11, 10, 10, 7, 6, 15, 10, 13, 14, 16, 6, 14, 13, 11, 6, 11, 13, 11, 11, 10, 9, 11, 10, 7, 11, 1, 15, 17, 10, 18, 7, 17, 13, 14, 13, 11, 16, 19, 7, 11, 11, 13, 9, 18, 15, 17, 20, 21, 11, 11, 10, 21, 13, 11, 21, 17, 11, 21, 11, 10, 11, 20, 5

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

Restricted growth sequence transform of the function f(n) = A335880(A088580(n)).

For all i, j:

A324400(i) = A324400(j) => a(i) = a(j),

a(i) = a(j) => A336694(i) = A336694(j),

a(i) = a(j) => A336695(i) = A336695(j).

LINKS

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

Index entries for sequences related to sigma(n)

PROG

(PARI)

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)];

v336926 = rgs_transform(vector(up_to, n, Aux335880(1+sigma(n))));

A336926(n) = v336926[n];

CROSSREFS

Cf. A000203, A088580, A329697, A331410, A332459, A335880, A336694, A336695.

Cf. also A336925.

Sequence in context: A367860 A151550 A097003 * A193788 A109447 A088261

Adjacent sequences: A336923 A336924 A336925 * A336927 A336928 A336929

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 10 2020

STATUS

approved