The gist below disables the user notification sent by the Series Add On for Paid Memberships Pro.

pmpro_disable_series_new_content_email.php

<?php
/**
 * pmpro_disable_series_new_content_email The gist below disables the user notification sent by the Series Add On for Paid Memberships Pro.
 *
 * Add this code to your PMPro Customizations Plugin
 * https://www.paidmembershipspro.com/create-a-plugin-for-pmpro-customizations/
 *
 */
function pmpro_disable_series_new_content_email( $recipient, $email ) {
	if( $email->template == 'new_content' ) {
		$recipient = NULL;
	}
	return $recipient;
}
add_filter( 'pmpro_email_recipient', 'pmpro_disable_series_new_content_email', 10, 2 );