A305898 Filter sequence combining prime signature of n (A046523) and similar signature (A284011) obtained when Stern polynomial B(n,x) is factored over Z.

1, 2, 2, 3, 2, 4, 2, 5, 3, 4, 2, 6, 2, 4, 4, 7, 2, 6, 2, 6, 4, 4, 2, 8, 9, 4, 5, 6, 2, 10, 2, 11, 4, 4, 4, 12, 2, 4, 4, 8, 2, 10, 2, 6, 6, 4, 2, 13, 3, 14, 4, 6, 2, 8, 15, 8, 4, 4, 2, 16, 2, 4, 17, 18, 15, 10, 2, 6, 4, 10, 2, 19, 2, 4, 6, 6, 15, 10, 2, 13, 20, 4, 2, 16, 4, 4, 4, 8, 2, 16, 15, 6, 4, 4, 15, 21, 2, 6, 6, 22, 2, 10, 2, 8, 10

Offset

1,2

Comments

Restricted growth sequence transform of ordered pair [A046523(n), A284011(n)].

For all i, j: a(i) = a(j) => A305892(i) = A305892(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; };
pfps(n) = { my(f=factor(n)); sum(i=1, #f~, f[i, 2] * 'x^(primepi(f[i, 1])-1)); };
A284010(n) = { if(!bitand(n, (n-1)), 0, my(p=0, f=vecsort(factor(pfps(n))[, 2], , 4)); prod(i=1, #f, (p=nextprime(p+1))^f[i])); }
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A260443(n) = if(n<2, n+1, if(n%2, A260443(n\2)*A260443(n\2+1), A003961(A260443(n\2))));
A284011(n) = A284010(A260443(n));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
Aux305898(n) = [A046523(n), A284011(n)];
v305898 = rgs_transform(vector(up_to, n, Aux305898(n)));
A305898(n) = v305898[n];

Crossrefs

Cf. A046523, A284011, A305892, A305899.

Cf. also A305790.

Sequence in context: A369760 A305899 A101296 * A181819 A302046 A077462

Adjacent sequences: A305895 A305896 A305897 * A305899 A305900 A305901

Keyword

nonn

Author

Antti Karttunen, Jul 01 2018

Status

approved