A095724 Fixed points of 1+Phi power sigma function 1PhiPsigma: if j = Product p_i^r_i then 1PhiPsigma(j) = Product {Sum p_i^r_i, 0 <= s_i < r_i, s_i is 0 or coprime to r_i} 1PhiPsigma(j) = j.

12, 56, 528, 992, 6720, 16256, 666624, 67100672

Offset

1,1

Comments

Factorizations: 2^2*3, 2^3*7, 2^4*3*11, 2^5*31, 2^6*3*5*7, 2^7*127, 2^10*3*7*31. If m is a perfect number then 2*m is a term of the sequence. Examples: 2^2*3, 2^3*7, 2^5*31, 2^7*127, .... If a(n)=2^r*k, GCD(2^r,k)=1, then k is squarefree.

Links

Table of n, a(n) for n=1..8.

Example

1 + PhiPsigma(2^5*3^4) = (1 + 2 + 2^2 + 2^3 + 2^4)*(1 + 3 + 3^3) = 961.
All exponents of the terms are 0 or coprime to the powers of corresponding prime factors of 2^5*3^3.

Crossrefs

Cf. A061389, A095723.

Sequence in context: A081756 A307741 A027147 * A225880 A224832 A139256

Adjacent sequences: A095721 A095722 A095723 * A095725 A095726 A095727

Keyword

nonn,more

Author

Yasutoshi Kohmoto, Jul 08 2004

Extensions

a(8) from Jud McCranie, Jul 16 2004

Status

approved