A365430 a(n) = A156552(gcd(n, A005940(n))), and A156552 is the inverse of offset-0 version of Doudna-sequence A005940.

0, 1, 2, 3, 4, 5, 0, 7, 0, 9, 0, 11, 0, 1, 2, 15, 0, 1, 0, 19, 8, 1, 0, 23, 0, 1, 2, 3, 0, 5, 0, 31, 0, 1, 0, 3, 0, 1, 2, 39, 0, 17, 0, 3, 4, 1, 0, 47, 0, 1, 2, 3, 0, 5, 4, 7, 0, 1, 0, 11, 0, 1, 6, 63, 0, 1, 0, 3, 0, 1, 0, 7, 0, 1, 10, 3, 16, 5, 0, 79, 0, 1, 0, 35, 4, 1, 2, 7, 0, 9, 8, 3, 0, 1, 4, 95, 0, 1, 34, 3

Offset: 1

Author

Antti Karttunen, Sep 07 2023

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A005940, A364500, A341520, A365432.

Programs

PARI

A156552(n) = {my(f = factor(n), p, 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
A364500(n) = { my(orgn=n,p=2,rl=0,z=1); n--; while(n, if(!(n%2), p=nextprime(1+p), rl++; if(1==(n%4), z *= p^min(rl,valuation(orgn,p)); rl=0)); n>>=1); (z); };
A365430(n) = A156552(A364500(n));

Formula

a(n) = A156552(A364500(n)).

For all n >= 1, a(n) <= n-1 and A341520(a(n), A365432(n)) = n-1.