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A305898
Filter sequence combining prime signature of n (A046523) and similar signature (A284011) obtained when Stern polynomial B(n,x) is factored over Z.
2
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
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))));
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. also A305790.
Sequence in context: A369760 A305899 A101296 * A181819 A302046 A077462
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 01 2018
STATUS
approved