# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a075867 Showing 1-1 of 1 %I A075867 #12 Jun 09 2020 22:11:04 %S A075867 4,12,18,27,40,180,250,300,450,704,780,924,1120,1170,1320,1344,1386, %T A075867 1400,1950,1960,2025,2970,3125,3192,3234,3500,4080,4455,4725,4760, %U A075867 4896,5070,5082,5625,5720,6615,6860,7182,7280,7875,8250,8280,8505,8704 %N A075867 Numbers k such that tau(k) = sigma(sopf(k)). %H A075867 David A. Corneth, Table of n, a(n) for n = 1..10000 (first 6300 terms from Robert Israel) %e A075867 tau(40) = number of divisors of 40 = 8; sigma(sum of prime factors of 40) = sigma(2 + 5) = 8. Hence 40 is a term of the sequence. %p A075867 filter:= proc(n) uses numtheory; %p A075867 tau(n) = sigma(convert(factorset(n),`+`)) %p A075867 end proc: %p A075867 select(filter, [$1..10^4]); # _Robert Israel_, Jun 09 2020 %t A075867 Select[Range[2, 10^4], DivisorSigma[1, Apply[Plus, Transpose[FactorInteger[ # ]][[1]]]] == DivisorSigma[0, # ] &] %o A075867 (PARI) is(n) = my(f = factor(n)); numdiv(f) == sigma(vecsum(f[, 1])) \\ _David A. Corneth_, Jun 09 2020 %Y A075867 Cf. A000005 (tau), A000203 (sigma), A000586, A008472 (sopf). %K A075867 nonn %O A075867 1,1 %A A075867 _Joseph L. Pe_, Oct 15 2002 %E A075867 Offset changed by _Robert Israel_, Jun 09 2020 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE