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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.
3
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.
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
KEYWORD
nonn
AUTHOR
Walter Nissen, May 20 2004
EXTENSIONS
Name clarified by Antti Karttunen, Feb 24 2020
STATUS
approved