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

1,3

Links

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

Formula

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

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

Prog

(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));

Crossrefs

Cf. A005940, A364500, A341520, A365432.

Sequence in context: A095874 A279385 A267000 * A224892 A351233 A265517

Adjacent sequences: A365427 A365428 A365429 * A365431 A365432 A365433

Keyword

nonn

Author

Antti Karttunen, Sep 07 2023

Status

approved