A318890 Filter sequence combining the prime signature of n (A046523) with the prime signature of its conjugated prime factorization (A278221).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 10, 15, 16, 12, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 14, 33, 34, 35, 36, 37, 38, 39, 40, 41, 18, 42, 43, 44, 45, 18, 46, 47, 48, 22, 31, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 39, 63, 64, 65, 66, 18, 67, 20, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 53, 36, 80, 81, 82, 83, 84, 85, 26, 86, 87, 88, 89, 90, 91, 39

Offset

1,2

Comments

Restricted growth sequence transform of A286454.

For all i, j: a(i) = a(j) => A318891(i) = A318891(j).

Links

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

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; };
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
A122111(n) = if(1==n, n, prime(bigomega(n))*A122111(A064989(n)));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A278221(n) = A046523(A122111(n));
A318890aux(n) = [A046523(n), A278221(n)];
v318890 = rgs_transform(vector(up_to, n, A318890aux(n)));
A318890(n) = v318890[n];

Crossrefs

Cf. A046523, A101296, A278221, A286454, A286621, A318891.

Sequence in context: A297248 A043274 A318891 * A124196 A293704 A322021

Adjacent sequences: A318887 A318888 A318889 * A318891 A318892 A318893

Keyword

nonn

Author

Antti Karttunen, Sep 16 2018

Status

approved