login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A280712 Inverse Euler transform of A280611. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A123022 A072943 A072175 * A306607 A268611 A092147

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 14 13:12 EDT 2020. Contains 336480 sequences. (Running on oeis4.)