A280712 Inverse Euler transform of A280611.

2, 1, 0, 1, 0, 4, 0, 1, 0, 2, 0, 2, 0, 0, 0, 1, 0, 4, 0, 3, 0, 2, 0, 4, 0, 0, 0, 2, 0, 2, 0, 1, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 0, 1, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 0, 1, 0, 2, 0, 7, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 9, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 6, 0, 0, 0, 4, 0, 2, 0, 1, 0

Offset

1,1

Comments

a(n) = b(n) for n odd, a(n) = b(n) - b(n/2) for n even >= 2, where b(n) = A014197(n) = the number of m with phi(m) = n.

Note that a(n) = 0 for all odd n > 1, and so a(n) = b(n) for n >= 3, n not a multiple of 4.

Links

Antti Karttunen, Table of n, a(n) for n = 1..20160

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Formula

Euler transform of sequence = Product_{k>=1} (1-x^k)^(-a(k)) is the g.f. of A280611.

Example

a(4) = #{m:phi(m) = 4} - #{m:phi(m) = 2} = #{5,8,10,12} - #{2,4,6} = 4-3 = 1.

Prog

(PARI)
A014197(n, m=1) = { n==1 && return(1+(m<2)); my(p, q); sumdiv(n, d, if( d>=m && isprime(d+1), sum( i=0, valuation(q=n\d, p=d+1), A014197(q\p^i, p))))}; \\ From A014197
A280712(n) = if(n%2, A014197(n), A014197(n)-A014197(n/2)); \\ Antti Karttunen, Nov 09 2018

Crossrefs

Cf. A014197, A280611.

Sequence in context: A072943 A372596 A072175 * A363926 A306607 A268611

Adjacent sequences: A280709 A280710 A280711 * A280713 A280714 A280715

Keyword

easy,nonn

Author

Christopher J. Smyth, Jan 07 2017

Extensions

More terms from Antti Karttunen, Nov 09 2018

Status

approved