MathDB

Silly construction problem - power sum of n

Source: Kürschák 1985, problem 2

July 27, 2014

number theory unsolvednumber theory

Problem Statement

For every

n\in\mathbb{N}

, define the power sum of

n

as follows. For every prime divisor

p

of

n

, consider the largest positive integer

k

for which

p^k\le n

, and sum up all the

p^k

's. (For instance, the power sum of

100

is

2^6+5^2=89

.) Prove that the power sum of

n

is larger than

n

for infinitely many positive integers

n

.

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