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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.
1
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.
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
Sequence in context: A081756 A307741 A027147 * A225880 A224832 A139256
KEYWORD
nonn,more
AUTHOR
Yasutoshi Kohmoto, Jul 08 2004
EXTENSIONS
a(8) from Jud McCranie, Jul 16 2004
STATUS
approved