No. The pervy sage, aka Jaraiya, was the 4th Hokage's Sensei, not his father.
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Naruto becomes a sage after he finds out that the pervy sage had died nd the elder frog that trained him uses toad oil and naruto becomes a sage he uses this power to fight pain,
Jirya dies in ep 132 of Naruto Shippuden
yes he dies because of his student (pein) who broke his sensei throat and let him drown
Ero-sennin (translated pervy sage or perverted sage/wiseman) is Naruto's nickname for Jiraiya, his last human sensei and also the one who trained his father, the 4th hokage. Naruto mastered the sage arts from the elder toad. Jiraiya is also Naruto's godfather, but Naruto is more like Jiraiya's grandson as mentioned by Jiraiya. Notes: 1. Naruto is one of the few male characters still alive who shows any interest in the opposite sex, so there is some hope of him becoming perverted. Sexy Jutsu!!! 2. As far as character development goes; Naruto has surpassed, in one way or another, Kakashi, the 4th Hokage, and now even Jiraiya. Expect him to become godly in the next few chapters and then "broken" when he studies his father's sealing scrolls. This manga will climax soon hopefully.
I don't think they tell you who Konohamaru's father is. I honestly think it's weird that the 3rd is Konohamaru's grandfather, and Asuma's dad, and Asuma is Konohamaru's uncle... maybe he doesn't have one?