A062830 a(n) = n - phi(n) + 1.

1, 2, 2, 3, 2, 5, 2, 5, 4, 7, 2, 9, 2, 9, 8, 9, 2, 13, 2, 13, 10, 13, 2, 17, 6, 15, 10, 17, 2, 23, 2, 17, 14, 19, 12, 25, 2, 21, 16, 25, 2, 31, 2, 25, 22, 25, 2, 33, 8, 31, 20, 29, 2, 37, 16, 33, 22, 31, 2, 45, 2, 33, 28, 33, 18, 47, 2, 37, 26, 47, 2

Offset

1,2

Comments

This is the cototient(A051953) + 1. If n = p*q for different primes p and q, a(n) = p + q. - Wesley Ivan Hurt, Aug 27 2013

If n is the product of twin primes, (a(n) +- 2)/2 gives the two primes. - Wesley Ivan Hurt, Sep 06 2013

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = A051953(n) + 1 = n - A000010(n) + 1. a(A006881(n)) = A008472(A006881(n)). - Wesley Ivan Hurt, Aug 27 2013

a(n) = 2*A067392(n)/n for n > 1. - Robert G. Wilson v, Jul 16 2019

Example

a(10) = 7, since 10 - phi(10) + 1 = 10 - 4 + 1 = 7.  Also, since 10 is a squarefree semiprime, 7 represents the sum of the distinct prime factors of 10.

Maple

with(numtheory); seq(k - phi(k) + 1, k = 1..70); # Wesley Ivan Hurt, Aug 27 2013

Mathematica

Table[n - EulerPhi[n] + 1, {n, 100}] (* Wesley Ivan Hurt, Aug 27 2013 *)

Prog

(PARI) j=[]; for(n=1, 200, j=concat(j, eulerphi(n)-n-1)); j

Crossrefs

Cf. A000010, A006881, A008472, A051953.

Sequence in context: A298423 A319810 A325250 * A322366 A363724 A345268

Adjacent sequences: A062827 A062828 A062829 * A062831 A062832 A062833

Keyword

easy,nonn

Author

Jason Earls, Jul 20 2001

Status

approved