A303772 Inverse of A303771.

0, 1, 3, 5, 9, 2, 17, 6, 33, 10, 65, 4, 129, 18, 12, 257, 513, 34, 1025, 14, 20, 66, 2049, 7, 4097, 130, 36, 22, 8193, 11, 16385, 258, 68, 514, 26, 38, 32769, 1026, 132, 15, 65537, 19, 131073, 70, 42, 2050, 262145, 260

Offset: 1

Author

Antti Karttunen, May 02 2018

Keywords

• nonn
• more

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A052331, A303768.

Programs

PARI

default(parisizemax,2^31);
up_to_e = 18;
up_to = (2 + 2^up_to_e);
v050376 = vector(2+up_to_e);
A050376(n) = v050376[n];
ispow2(n) = (n && !bitand(n,n-1));
i = 0; for(n=1,oo,if(ispow2(isprimepower(n)), i++; v050376[i] = n); if(i == 2+up_to_e,break));
A052330(n) = { my(p=1,i=1); while(n>0, if(n%2, p *= A050376(i)); i++; n >>= 1); (p); };
A053669(n) = forprime(p=2, , if (n % p, return(p))); \\ From A053669
v303760 = vector(up_to);
m_inverses = Map();
prev=1; for(n=1,up_to,fordiv(prev,d,if(!mapisdefined(m_inverses,d),v303760[n] = d;mapput(m_inverses,d,n);break)); if(!v303760[n], apu = prev; while(mapisdefined(m_inverses,try = prev*A053669(apu)), apu *= A053669(apu)); v303760[n] = try; mapput(m_inverses,try,n)); prev = v303760[n]);
A303760(n) = v303760[n+1];
A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
A303771(n) = A052330(A048675(A303760(n)));
m303772 = Map();
for(n=0,up_to-1,mapput(m303772,A303771(n),n));
A303772(n) = mapget(m303772,n);

Formula

a(n) = A303768(A052331(n)).