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A095724 Fixed point of 1+Phi power sigma function: if n=Product p_i^r_i then 1PhiPsigma(n)= Product {Sum p_i^r_i, 0<=s_i<r_i, s_i is 0 or coprime to r_i} 1PhiPsigma(n)=n. 1
12, 56, 528, 992, 6720, 16256, 666624, 67100672 (list; graph; refs; listen; history; text; internal format)
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 exists on 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

AUTHOR

Yasutoshi Kohmoto, Jul 08 2004

EXTENSIONS

67100672 from Jud McCranie, Jul 16 2004

STATUS

approved

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Last modified October 14 08:54 EDT 2019. Contains 327995 sequences. (Running on oeis4.)