If this is Barry, then the citizenship is invalid because his birth did not come long enough after his mother’s sixteenth birthday for his birth to her to confer U.S. citizenship on him. And that wouldn’t have happened through his putative father since the statutory rapist was never a U.S. citizen. And even if his father had been Frank Marshall Davis, FMD had not married Stanley Ann.
Under section 322 of the INA of 1952 as the son/child of a US citizen, Obama would have been able to be naturalized upon application by his mother, only requirement would be the application and that he was admitted lawfully (with a few inapplicable exceptions) because of his tender years other requirements such as good moral character, residency are waived...he could then be issued proof of citizenship while an infant. He would then be a Naturalized USC.
http://library.uwb.edu/guides/usimmigration/66%20stat%20163.pdf
(page 246 of pdf, I can’t copy & paste it maybe someone else can)
http://www.uscis.gov/ilink/docView/AFM/HTML/AFM/0-0-0-1/0-0-0-20833/0-0-0-20835.html
(this law has changed from 1952 but primarily added to allow for grandparents to meet residency requirements and children to obtain USC while still abroad)
............
He also could have been a citizen if he was born out of wedlock and his mother was a US citizen Section 301 of INA 1952, he would be a citizen at birth and able to obtain a Certificate of Citizenship (no decision has been made whether that would be NBC for Presidential eligibility question)
If his father was a USC out of wedlock under section 309 and he could gain citizenship if he was legitimized prior to age 21(not necessary if his mother was USC with one year continuous physical presence in US prior to his birth, which she was.