A365457 a(n) = A365456(A005940(n)), where A365456(n) = A156552(2*n) / gcd(sigma(n), A156552(2*n)), and A156552 is the inverse of offset-0 version of Doudna-sequence, A005940.

1, 1, 5, 1, 3, 11, 1, 1, 17, 19, 7, 23, 25, 9, 29, 1, 11, 35, 37, 13, 41, 43, 15, 47, 49, 17, 53, 55, 19, 59, 61, 1, 65, 67, 23, 71, 73, 25, 77, 79, 27, 83, 85, 29, 89, 7, 31, 95, 97, 11, 101, 103, 35, 107, 109, 37, 113, 115, 3, 17, 11, 41, 125, 1, 43, 131, 19, 45, 137, 139, 47, 143, 145, 49, 149, 151, 51, 155

Offset

1,3

Links

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

Index entries for sequences related to binary expansion of n

Index entries for sequences related to sigma(n)

Formula

a(n) = (2*n-1) / gcd(2*n-1, A324054(n-1)).

Prog

(PARI)
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
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
A365456(n) = { my(u=A156552(2*n)); (u/gcd(u, sigma(n))); };
A365457(n) = A365456(A005940(n));

Crossrefs

Cf. A000203, A005940, A156552, A324054, A365456.

Sequence in context: A244350 A176321 A248130 * A365456 A134894 A143700

Adjacent sequences: A365454 A365455 A365456 * A365458 A365459 A365460

Keyword

nonn

Author

Antti Karttunen, Sep 10 2023

Status

approved