A365432 a(n) = A156552(A364502(n)), where A364502(n) = A005940(n) / gcd(n, A005940(n)), and A156552 is the inverse of offset-0 version of Doudna-sequence A005940.

0, 0, 0, 0, 0, 0, 6, 0, 8, 0, 10, 0, 12, 6, 6, 0, 16, 8, 18, 0, 4, 10, 22, 0, 24, 12, 12, 6, 28, 6, 30, 0, 32, 16, 34, 8, 36, 18, 18, 0, 40, 4, 42, 10, 20, 22, 46, 0, 48, 24, 24, 12, 52, 12, 22, 6, 56, 28, 58, 6, 60, 30, 14, 0, 64, 32, 66, 16, 68, 34, 70, 8, 72, 36, 16, 18, 12, 18, 78, 0, 80, 40, 82, 4, 40, 42, 42, 10

Offset

1,7

Links

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

Formula

For all n >= 1, a(n) <= n-1 and A341520(a(n), A365430(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
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A364502(n) = { my(u=A005940(n)); (u / gcd(n, u)); };
A365432(n) = A156552(A364502(n));

Crossrefs

Cf. A005940, A364500, A341520, A365430, A365431 (rgs-transform).

Sequence in context: A201521 A011393 A066362 * A279929 A244812 A083680

Adjacent sequences: A365429 A365430 A365431 * A365433 A365434 A365435

Keyword

nonn

Author

Antti Karttunen, Sep 07 2023

Status

approved