A353273 a(n) = (A332449(n) / gcd(n, A332449(n))) - n, where A332449(n) = A005940(1+(3*A156552(n))).

0, 0, 0, 1, 0, 2, 0, 7, -2, 8, 0, -1, 0, 36, 12, 29, 0, 2, 0, 5, 54, 76, 0, -13, -14, 216, 8, 7, 0, 2, 0, 103, 114, 304, 90, 41, 0, 540, 324, 35, 0, -18, 0, 11, -32, 676, 0, -15, -36, -8, 456, 13, 0, -34, 190, 49, 810, 1000, 0, -43, 0, 1620, -14, 341, 540, 134, 0, 17, 1014, 92, 0, 5, 0, 1848, -12, 19, 266, 314, 0, 145

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = A353272(n) - n.

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 };
A332449(n) = A005940(1+(3*A156552(n)));
A353273(n) = { my(u=A332449(n)); (u / gcd(n, u))-n; };

Crossrefs

Cf. A005940, A156552, A332449, A353270, A353271, A353272, A353274, A353275.

Sequence in context: A198108 A300704 A300702 * A105394 A196767 A307216

Adjacent sequences: A353270 A353271 A353272 * A353274 A353275 A353276

Keyword

sign,less

Author

Antti Karttunen, Apr 09 2022

Status

approved