A300247 Restricted growth sequence transform of A286457(n), filter combining A078898(n) and A246277(n).

1, 2, 2, 3, 2, 4, 2, 5, 3, 6, 2, 7, 2, 8, 4, 9, 2, 10, 2, 11, 12, 13, 2, 14, 3, 15, 16, 17, 2, 18, 2, 19, 20, 21, 4, 22, 2, 23, 24, 25, 2, 26, 2, 27, 28, 29, 2, 30, 3, 31, 32, 33, 2, 34, 12, 35, 36, 37, 2, 38, 2, 39, 40, 41, 42, 43, 2, 44, 45, 46, 2, 47, 2, 48, 49, 50, 4, 51, 2, 52, 53, 54, 2, 55, 56, 57, 58, 59, 2, 60, 12, 61, 62, 63, 64, 65, 2, 66

Offset

1,2

Comments

For all i, j:

a(i) = a(j) => A280492(i) = A280492(j).

a(i) = a(j) => A300248(i) = A300248(j).

The latter follows because A046523(n) = A046523(2*A246277(n)).

Links

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

Index entries for sequences computed from indices in prime factorization

Example

a(65) = a(119) (= 42) because A078898(65) = A078898(119) = 5 (both numbers occur in column 5 of A083221) and because A246277(65) = A246277(119) = 7 (both numbers occur in column 7 of A246278). Note that 65 = 5*13 = prime(3)*prime(6) and 119 = 7*17 = prime(4)*prime(7) = A003961(65). A246277(n) contains complete information about the (relative) differences between prime indices in the prime factorization of n.

Prog

(PARI)
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; };
write_to_bfile(start_offset, vec, bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A020639(n) = { if(1==n, n, vecmin(factor(n)[, 1])); };
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)};
A078898(n) = { if(n<=1, n, my(spf=A020639(n), k=1, m=n/spf); while(m>1, if(A020639(m)>=spf, k++); m--); (k)); }; \\ Antti Karttunen, Mar 03 2018
A246277(n) = { if(1==n, 0, while((n%2), n = A064989(n)); (n/2)); };
A286457(n) = if(1==n, 0, (1/2)*(2 + ((A078898(n)+A246277(n))^2) - A078898(n) - 3*A246277(n)));
write_to_bfile(1, rgs_transform(vector(65537, n, A286457(n))), "b300247.txt");

Crossrefs

Cf. A078898, A246277, A286457.

Cf. also A300248, A280492.

Sequence in context: A305897 A355834 A300248 * A318887 A305975 A304751

Adjacent sequences: A300244 A300245 A300246 * A300248 A300249 A300250

Keyword

nonn,look

Author

Antti Karttunen, Mar 03 2018

Status

approved