A366219 Smallest positive integer whose smallest coprime divisor shift is n.

1, 3, 91, 325, 2093, 1001, 12025, 1045, 4945, 6391, 189, 455, 245, 11825, 128843, 368809, 273, 1295, 14495, 37961, 252263, 91375, 595, 13013, 46189, 104951, 63875, 136345, 42237, 22253, 192647, 18655, 8225, 194545, 200629, 192907, 27625, 1911, 464783, 27797

Offset

0,2

Comments

A nonnegative number s is a coprime divisor shift of n if GCD(d + s, n) = 1 for all divisors d of n. The coprime divisor shift of n is the infimum of the set of all nonnegative coprime divisor shifts of n.

Conjecture. Every positive integer s is the coprime divisor shift of a positive integer.

Links

M. Farrokhi D. G., Table of n, a(n) for n = 0..1000

Example

a(0) = 1 for GCD(1 + 0, 1) = 1.
a(1) = 3 for GCD(1 + 1, 3) = GCD(3 + 1, 3) = 1 but GCD(1 + 1, 2) > 1.
a(2) = 91 for GCD(d + 2, 91) = 1 for all divisors d = 1, 7, 13, 91 of 91, GCD(13 + 1, 91) > 1, and 91 is the smallest number with this property.

Prog

(PARI)
isds(k, s)={fordiv(k, d, if(gcd(d+s, k)<>1, return(0))); 1}
findds(k)={for(s=0, k-1, if(isds(k, s), return(s))); -1}
a(n)={for(k=1, oo, if(isds(k, n) && findds(k)==n, return(k)))} \\ Andrew Howroyd, Oct 05 2023

Crossrefs

Cf. A366251, A366330.

Sequence in context: A066751 A115886 A041439 * A300419 A156754 A331672

Adjacent sequences: A366216 A366217 A366218 * A366220 A366221 A366222

Keyword

nonn

Author

M. Farrokhi D. G., Oct 05 2023

Status

approved