A332816 a(n) = A156552(A332808(n)).

0, 1, 2, 3, 4, 5, 8, 7, 6, 9, 32, 11, 16, 17, 10, 15, 64, 13, 128, 19, 18, 65, 512, 23, 12, 33, 14, 35, 256, 21, 2048, 31, 66, 129, 20, 27, 1024, 257, 34, 39, 4096, 37, 8192, 131, 22, 1025, 32768, 47, 24, 25, 130, 67, 16384, 29, 68, 71, 258, 513, 131072, 43, 65536, 4097, 38, 63, 36, 133, 524288, 259, 1026, 41, 2097152, 55, 262144, 2049, 26, 515

Offset: 1

Author

Antti Karttunen, Feb 28 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A332815 (inverse permutation).

Cf. A070939, A156552, A332808, A332894, A332899.

Programs

PARI

up_to = 26927;
A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A332806list(up_to) = { my(v=vector(2), xs=Map(), lista=List([]), p,q,u); v[2] = 3; v[1] = 5; mapput(xs,1,1); mapput(xs,2,2); mapput(xs,3,3);  for(n=4,up_to, p = v[2-(n%2)]; q = nextprime(1+p); while(q%4 != p%4, q=nextprime(1+q)); v[2-(n%2)] = q; mapput(xs,primepi(q),n)); for(i=1, oo, if(!mapisdefined(xs, i, &u), return(Vec(lista)), listput(lista, prime(u)))); };
v332806 = A332806list(up_to);
A332806(n) = v332806[n];
A332808(n) = { my(f=factor(n)); f[,1] = apply(A332806,apply(primepi,f[,1])); factorback(f); };
A332816(n) = A156552(A332808(n));

Formula

a(n) = A156552(A332808(n)).

For n > 1, A070939(a(n)) = A332894(n).

For n >= 1: (Start)

A080791(a(n)) = A332899(n)-1.

Among many identities given in A156552 that apply here as well we have for example the following ones:

A000120(a(n)) = A001222(n).

A069010(a(n)) = A001221(n).

A106737(a(n)) = A000005(n).

(End)