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A344770
Ordinal transform of A011772.
4
1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 3, 1, 4, 1, 1, 2, 2, 1, 4, 1, 1, 3, 5, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 6, 1, 2, 2, 1, 1, 3, 1, 3, 2, 2, 1, 2, 1, 2, 3, 1, 1, 4, 1, 1, 1, 2, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 2, 1, 2, 3, 1, 4, 1, 4, 1, 1, 1, 2, 2
OFFSET
1,6
COMMENTS
Number of values of k, 1 <= k <= n, with A011772(k) = A011772(n).
a(n) = 1 for all powers of primes, A000961. Ones occur on some other positions as well: 15, 22, 35, 38, 42, 44, 45, 46, 51, 52, 54, 65, ...
LINKS
FORMULA
a(n) >= A344590(n).
MATHEMATICA
A011772[n_] := For[m = 1, True, m++, If[Divisible[m(m+1)/2, n], Return[m]]];
b[_] = 0;
a[n_] := a[n] = With[{t = A011772[n]}, b[t] = b[t]+1];
Array[a, 105] (* Jean-François Alcover, Dec 21 2021 *)
PROG
(PARI)
up_to = 65537;
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; };
A011772(n) = { if(n==1, return(1)); my(f=factor(if(n%2, n, 2*n)), step=vecmax(vector(#f~, i, f[i, 1]^f[i, 2]))); forstep(m=step, 2*n, step, if(m*(m-1)/2%n==0, return(m-1)); if(m*(m+1)/2%n==0, return(m))); }; \\ From A011772
v344770 = ordinal_transform(vector(up_to, n, A011772(n)));
A344770(n) = v344770[n];
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, May 30 2021
STATUS
approved