"giving joy" (Sanskrit harsha, joy +da taddhita pratyaya, causative); these are defined by the property that they are divisible by the sum of their digits. Thus 12, which is divisible by 1 + 2 = 3, is a harshad number. These were later also called Niven numbers after 1977 lecture on these by the Canadian mathematician Ivan M. Niven. Numbers which are harshad in all bases (only 1, 2, 4, and 6) are called all-harshad numbers. Much work has been done on harshad numbers, and their distribution, frequency, etc. are a matter of considerable interest in number theory today. Demlo number Kaprekar also studied the Demlo numbers, named after a train station Demlo (now called Dombivili) 30 miles from Bombay on the then G. I. P. Railway where he had the idea of studying them. The best known of these are the Wonderful Demlo numbers 1, 121, 12321, 1234321, …, which are the squares of the repunits 1, 11, 111,1111, …. See also Prahalad Chunnilal Vaidya References External links "Mysterious number 6174" Numberphile (Dec 5, 2011) 6174 a YouTube video by Numberphile 1905 births 1986 deaths 20th-century Indian mathematicians Indian number theorists Recreational mathematicians Magic squares People from Thane district Scientists from Maharashtra