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By comparing Green functions of multi-circled plurisubharmonic singularitiesin the n-domensional complex space to their indicators, we obtain formulas forthe higher Lelong numbers and integrability index for such singularities andextend Howald's result on multiplier ideals for monomial ideals tomulti-circled singularities. This also leads to an elementary proof of therelations between the k-th Lelong numbers and the integrability index. For k=1and arbitrary plurisubharmonic functions the inequality is due to Skoda, andfor k=n and any plurisubharmonic function with isolated singularity therelation is due to Demailly. We also describe multi-circled functions for whichthe inequalities are equalities. By a reduction to Demailly's inequality weprove these inequalities in the general case of plurisubharmonic functions aswell. In addition, we get a description of all plurisubharmonic singularitieswhose integrability index is given by the lower bound in Skoda's inequality.

Multi-circled singularities, Lelong numbers, and integrability index