A094701 Smallest linear combination of phi(n) and sigma(n) with nonnegative coefficients: a(n) = Min_{x>=0,y>=0} (x+y) for which x*phi(n) + y*sigma(n) is a multiple of n.

1, 2, 2, 2, 2, 1, 2, 2, 3, 3, 2, 3, 2, 4, 5, 2, 2, 3, 2, 4, 7, 4, 2, 2, 5, 4, 3, 1, 2, 5, 2, 2, 9, 4, 18, 3, 2, 4, 9, 4, 2, 7, 2, 6, 3, 4, 2, 3, 7, 5, 9, 5, 2, 3, 7, 3, 9, 4, 2, 5, 2, 4, 7, 2, 11, 7, 2, 9, 9, 10, 2, 3, 2, 4, 12, 4, 10, 7, 2, 5, 3, 4, 2, 3, 13, 4, 9, 4, 2, 5, 9, 9, 9, 4, 19, 3, 2, 7, 5, 5, 2, 7

Offset

1,2

Comments

a(n) is a generalization of the multiperfect numbers in A007691.

Links

Antti Karttunen, Table of n, a(n) for n = 1..12857

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Formula

a(multiperfect) = 1.

a(prime) = 2 as 1*phi(prime) + 1*sigma(prime) and 1+1 = 2.

For primes > 5, a(2*prime) = 4.

Example

a(6) = 1 as 1*sigma(6) is a multiple of 6.
a(4) = 2 as 2*phi(4) + 0*sigma(4) = 4. - Example added by Antti Karttunen, Feb 24 2020
a(14) = 4 as 3*phi(14) + 1*sigma(14) = 3*6 + 24 = 3*14, where 3+1 = 4.

Prog

(PARI) A094701(n) = { my(x=eulerphi(n), y=sigma(n)); for(s=1, oo, for(t=0, s, if(!(((t*x)+((s-t)*y))%n), return(s)))); }; \\ Antti Karttunen, Feb 24 2020

Crossrefs

Cf. A000010, A000203, A000396, A005820, A007691 (positions of ones), A027687, A046060, A046061.

Sequence in context: A355832 A055020 A052435 * A210452 A347037 A240301

Adjacent sequences: A094698 A094699 A094700 * A094702 A094703 A094704

Keyword

nonn

Author

Walter Nissen, May 20 2004

Extensions

Name clarified by Antti Karttunen, Feb 24 2020

Status

approved