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

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

1,3

Comments

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).

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; };
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];

Crossrefs

Cf. also A336926.

Sequence in context: A364577 A286449 A318310 * A331744 A323892 A318311

Adjacent sequences: A336922 A336923 A336924 * A336926 A336927 A336928

Keyword

nonn

Author

Antti Karttunen, Aug 10 2020

Status

approved