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 A252056 a(n) is the least m such that m = A001065(j) = A001065(k) where j != k, A000005(j) = A000005(k) = n; or 0 if no such m exists. 0
 0, 1, 0, 13, 0, 73, 0, 106, 9064940, 4001, 0, 396, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS When n>2 and A001055(n)=1, then a(n)=0; because in that case, only a prime^n has n divisors, and then it is not possible to get twice the same value for sigma(x)-x. This happens for n=3, 5, 7, 11, 13, 17, 19, 23, 29, ... - Michel Marcus, Dec 16 2014 Note that for n=8, j and k do not have the same prime signature. - Michel Marcus, Dec 17 2014 LINKS EXAMPLE For n=2, all primes have 2 divisors and satisfy sigma(x)-x=1, so a(2) = 1. For n=4, 27 and 35 have 4 divisors and the sum of their proper divisors is 13 for both (1+3+9 and 1+5+7). For n=6, 98 and 175 have 6 divisors and the sum of their proper divisors is 73 for both (1+2+7+14+49 and 1+5+7+25+35). For n=8, 104 and 110 have 8 divisors and the sum of their proper divisors is 106 for both (1+2+4+8+13+26+52 and 1+2+5+10+11+22+55). For n=9, 163^2*167^2 and 61^2*353^2 have 9 divisors and the sum of their proper divisors is 9064940 for both. For n=10, 7203 and 7857 have 10 divisors and the sum of their proper divisors is 4001 for both. For n=12, 276 and 306 have 12 divisors and the sum of their proper divisors is 396 for both. CROSSREFS Cf. A000005 (number of divisors of n), A001065 (sum of proper divisors of n). Cf. A001055, A048138, A152454. Sequence in context: A065112 A114783 A094902 * A096069 A180265 A165400 Adjacent sequences:  A252053 A252054 A252055 * A252057 A252058 A252059 KEYWORD nonn,more AUTHOR Naohiro Nomoto, Dec 13 2014 EXTENSIONS a(9)-a(13) from Michel Marcus, Dec 16 2014 STATUS approved

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Last modified November 28 20:42 EST 2021. Contains 349415 sequences. (Running on oeis4.)