A319689 -id:A319689 - cp's OEIS frontend

A319694 Product of A078899(x) for all x encountered when map x -> A252463(x) is iterated, starting from x = A252463(n); a(1) = 1.

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 6, 1, 6, 1, 2, 2, 1, 1, 8, 6, 1, 6, 2, 1, 6, 1, 24, 2, 1, 6, 30, 1, 1, 2, 8, 1, 6, 1, 2, 8, 1, 1, 48, 30, 30, 2, 2, 1, 42, 6, 8, 2, 1, 1, 36, 1, 1, 8, 120, 6, 6, 1, 2, 2, 30, 1, 240, 1, 1, 30, 2, 30, 6, 1, 56, 24, 1, 1, 36, 6, 1, 2, 8, 1, 64, 30, 2, 2, 1, 6, 432, 1, 210, 8, 270, 1, 6, 1, 8, 36

Offset: 1

Antti Karttunen, Nov 21 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences computed from indices in prime factorization

Cf. A005940, A078899, A252463.

Cf. also A319689.

up_to = 16384;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
v078899 = ordinal_transform(vector(up_to,n,A006530(n)));
A078899(n) = v078899[n];
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)};
A252463(n) = if(!(n%2),n/2,A064989(n));
A319694(n) = { my(m=1); while(1<(n=A252463(n)), m *= A078899(n)); (m); };

A319679 Number of distinct prime signatures that occur when map x -> A268674(x) is iterated, starting from x = n, until an even number is reached; a(1) = 0 by convention.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2

Offset: 1

Antti Karttunen, Nov 20 2018

nonn

Number of distinct values that A046523 obtains when applied to n and all the terms above it in that column where it is located in array A083221.

Antti Karttunen, Table of n, a(n) for n = 1..32769

Cf. A046523, A083221, A268674.

Cf. also A319689.

up_to = 32769;
v268674 = readvec("./b268674_terms_only-32769.txt"); \\ Prepared from the b-file of A268674.
A268674(n) = v268674[n];
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A319679(n) = if(1==n,0,my(m=Map(),s,k=0); while(1,if(!mapisdefined(m,s=A046523(n)), mapput(m,s,s); k++); if(!(n%2), return(k)); n = A268674(n)));

cp's OEIS Frontend

A319694 Product of A078899(x) for all x encountered when map x -> A252463(x) is iterated, starting from x = A252463(n); a(1) = 1.

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