And on a side note, what other things influenced him to drop the bombs?
Not really, Russia was pretty much exhausted by the time the Nazis finally surrendered. Sure they could devote resources to fight in Japan but nothing significant for quite some time. Remember Russia is a VERY LONG country. It would take months to mobilze any sort of force. In addition how motivated would the Russians be after their campaign aganist the Germans? Everyone knew Japan was going lose the war, with or without the help of the soviet union.
What really motivated Truman decision was he understood that battle for man land Japan would be the bloodiest campaign in US History. It was estimated that a million American Service Members would die in the conflict millions more Japanese (both civilian and military) would also die. It was believed that if America could demonstrate their destructive power with just a single bomb it would motivate the Japan High Command to surrender earlier.
So Truman believed that he could scare the Japanese to not fight anymore, which considering the destructive capabilities of the bomb was a reasonable assumption which turned out to be true.
I believe the reason the Soviet Union involvement is often mentioned is because no one wanted the Soviets to have even more of a foot hold across the world. Saying "We need to win the war before the Soviets get involved" sped things along.
TL:DR Truman wanted to avoid the death of millions of lives both American and Japanese.