A095724 Fixed points of 1+Phi power sigma function 1PhiPsigma: integers m such that 1PhiPsigma(m) = m, where for j = Product p_i^r_i, 1PhiPsigma(j) = Product_i Sum_{0 <= s_i <= r_i, s_i is 0 or coprime to r_i} p_i^s_i.

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

Offset: 1

Author

Yasutoshi Kohmoto, Jul 08 2004

Keywords

• nonn
• more

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.

Examples

			1PhiPsigma(2^5*3^4) = (1 + 2 + 2^2 + 2^3 + 2^4)*(1 + 3 + 3^3) = 961.
		

Crossrefs

Cf. A061389, A095723.

Extensions

a(8) from Jud McCranie, Jul 16 2004

Edited by Max Alekseyev, Dec 04 2024