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 A045795 Unitary-sigma sigma multiply perfect numbers n such that usigma(sigma(n)) = m*n for some integer m, where if sigma(n) = product p(i)^r(i) then usigma(sigma(n)) = product (p(i)^r(i)+1). 3
 1, 2, 4, 8, 10, 16, 24, 27, 30, 54, 63, 64, 108, 126, 165, 238, 252, 360, 432, 504, 512, 660, 864, 952, 1008, 1536, 1728, 2016, 2464, 2640, 4032, 4096, 5544, 10560, 13824, 16728, 17640, 23040, 32256, 45500, 47360, 60928, 65536, 110592, 152064, 153600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Donovan Johnson, Table of n, a(n) for n = 1..100 EXAMPLE For example, sigma(10) = 18 = 2*3^2. Usigma(18) = (2+1)*(9+1) = 30, divisible by 10, so 10 is in the sequence. Sigma(24) = 60 = 2^2*3*5, usigma(60) = 5*4*6 = 120, divisible by 24, so 24 is in the sequence. PROG (PARI) for(n=1, 10^9, s=sigma(n); om=omega(s); f=factorint(s); pr=1; for(j=1, om, pr=pr*(f[j, 1]^f[j, 2]+1)); if(pr%n==0, print(n))) /* Donovan Johnson, Mar 12 2013 */ CROSSREFS Cf. A045796, A034448. Sequence in context: A102248 A161374 A272062 * A226816 A291165 A083655 Adjacent sequences:  A045792 A045793 A045794 * A045796 A045797 A045798 KEYWORD nonn AUTHOR EXTENSIONS Corrected and extended by Jud McCranie, Oct 28 2001 Missing first term added and offset corrected by Donovan Johnson, Mar 12 2013 STATUS approved

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Last modified November 13 10:29 EST 2019. Contains 329093 sequences. (Running on oeis4.)