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A318888
Filter sequence combining the 2-adic valuation of n (A007814) with the differences between odd primes in the prime factorization of n.
4
1, 2, 3, 4, 3, 5, 3, 6, 7, 5, 3, 8, 3, 5, 9, 10, 3, 11, 3, 8, 12, 5, 3, 13, 7, 5, 14, 8, 3, 15, 3, 16, 17, 5, 9, 18, 3, 5, 19, 13, 3, 20, 3, 8, 21, 5, 3, 22, 7, 11, 23, 8, 3, 24, 25, 13, 26, 5, 3, 27, 3, 5, 28, 29, 17, 30, 3, 8, 31, 15, 3, 32, 3, 5, 33, 8, 12, 34, 3, 22, 35, 5, 3, 36, 37, 5, 38, 13, 3, 39, 25, 8, 40, 5, 23, 41, 3, 11, 42, 18, 3, 43, 3, 13, 44
OFFSET
1,2
COMMENTS
Restricted growth sequence transform of an ordered pair [A007814(n), A318885(A000265(n))].
For all i, j: A305801(i) = A305801(j) => a(i) = a(j) => A305891(i) = A305891(j).
LINKS
PROG
(PARI)
up_to = 100000;
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; };
A000265(n) = (n/2^valuation(n, 2));
A007814(n) = valuation(n, 2);
A318885(n) = if(1==n, n, my(f=factor(n), m=2^f[1, 2], i=1); for(k=2, #f~, i += (f[k, 1]-f[k-1, 1]); m *= prime(i)^f[k, 2]); (m));
v318888 = rgs_transform(vector(up_to, n, [A007814(n), A318885(A000265(n))]));
A318888(n) = v318888[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 24 2018
STATUS
approved