Search: a366878 -id:a366878
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A366874
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Lexicographically earliest infinite sequence such that a(i) = a(j) => A366873(i) = A366873(j) for all i, j >= 0, where A366873 is the average of number of and sum of odd divisors of n as permuted by A163511.
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+10
5
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1, 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, 16, 1, 17, 9, 18, 5, 19, 10, 20, 3, 21, 11, 22, 6, 23, 12, 24, 2, 25, 13, 26, 7, 27, 14, 28, 4, 29, 15, 30, 8, 14, 16, 3, 1, 31, 17, 32, 9, 33, 18, 34, 5, 35, 19, 36, 10, 37, 20, 38, 3, 39, 21, 40, 11, 41, 22, 42, 6
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OFFSET
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0,4
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COMMENTS
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Restricted growth sequence transform of A366873.
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LINKS
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PROG
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(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; };
A113415(n) = if(n<1, 0, sumdiv(n, d, if(d%2, (d+1)/2)));
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
v366874 = rgs_transform(vector(1+up_to, n, A366873(n-1)));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A366875
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a(n) = A349915(A163511(n)), where A349915 is the Dirichlet inverse of the arithmetic mean between the number and sum of the odd divisors of n.
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+10
4
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1, -1, 0, -3, 0, 1, 3, -4, 0, -1, -1, -1, 0, 10, 4, -5, 0, -2, 1, -8, 0, 5, 1, -5, 0, -2, -10, 14, 0, 12, 5, -7, 0, -4, 2, -24, 0, 32, 8, -27, 0, 1, -5, 26, 0, 18, 5, -19, 0, 6, 2, 11, 0, -20, -14, 20, 0, -2, -12, 18, 0, 16, 7, -8, 0, -8, 4, -72, 0, 112, 24, -108, 0, -8, -32, 162, 0, 108, 27, -125, 0, 3, -1, 35, 0
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graph;
refs;
listen;
history;
text;
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OFFSET
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0,4
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LINKS
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PROG
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(PARI)
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A113415(n) = if(n<1, 0, sumdiv(n, d, if(d%2, (d+1)/2)));
memoA349915 = Map();
A349915(n) = if(1==n, 1, my(v); if(mapisdefined(memoA349915, n, &v), v, v = -sumdiv(n, d, if(d<n, A113415(n/d)*A349915(d), 0)); mapput(memoA349915, n, v); (v)));
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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A366880
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Lexicographically earliest infinite sequence such that a(i) = a(j) => A366879(i) = A366879(j) for all i, j >= 0.
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+10
2
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1, 2, 3, 4, 3, 5, 6, 7, 3, 3, 7, 8, 3, 9, 10, 11, 3, 3, 3, 3, 3, 12, 13, 14, 3, 15, 16, 17, 3, 18, 19, 20, 3, 3, 3, 3, 3, 3, 3, 3, 3, 21, 22, 23, 3, 24, 25, 26, 3, 3, 27, 28, 3, 29, 30, 31, 3, 32, 33, 34, 3, 17, 9, 25, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 35, 36, 3, 37, 38, 39, 3, 40, 41, 42, 3, 43
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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Restricted growth sequence transform of A366879.
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LINKS
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PROG
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(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; };
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A326938(n) = sumdiv(n, d, if(n/d%2, moebius(n/d)*moebius(d)*d));
v366880 = rgs_transform(vector(1+up_to, n, A366879(n-1)));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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