A281993
Integers m such that sigma(m) + sigma(2*m) = 6*m.
Original entry on oeis.org
10, 44, 184, 752, 12224, 49024, 12580864, 206158168064, 885443715520878608384, 226673591177468092350464, 232113757366000005450563584, 3894222643901120685369075227951104, 1020847100762815390371677078221595082752, 17126972312471518572699356075530215722269540352
Offset: 1
10 is a term since sigma(10) + sigma(20) = 60, that is 6*10.
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Select[Range[10^7], DivisorSigma[1, #] + DivisorSigma[1, 2 #] == 6 # &] (* Michael De Vlieger, Feb 04 2017 *)
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isok(n, h=2) = sigma(n) + sigma(h*n) == 2*n*(h+1);
A097214
Numbers m such that A076078(m) = m, where A076078(m) equals the number of sets of distinct positive integers with a least common multiple of m.
Original entry on oeis.org
1, 2, 4, 8, 10, 16, 32, 44, 64, 128, 184, 256, 512, 752, 1024, 2048, 4096, 8192, 12224, 16384, 32768, 49024, 61064, 65536, 131072, 262144, 524288, 981520, 1048576, 2097152, 4194304, 8388608, 12580864, 16777216, 33554432, 67108864, 134217728
Offset: 1
A total of 10 sets of distinct positive integers have a least common multiple of 10: {1,2,5}, {1,2,5,10}, {1,2,10}, {1,5,10}, {1,10}, {2,5}, {2,5,10}, {2,10}, {5,10} and {10}. Hence 10 is in the sequence.
A097416
Numbers n such that A076078(m)=n for some m, excluding powers of 2.
Original entry on oeis.org
10, 44, 184, 218, 400, 752, 3040, 3392, 3748, 12224, 27904, 49024, 57856, 61064, 64594, 196352, 226304, 253808, 785920, 954368, 981520, 1822720, 3144704, 12580864, 14630912, 15499264, 15722528, 16450240, 16700300, 31522816, 50327552
Offset: 1
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f[n_] := Block[{d = Divisors[n]}, Plus @@ (MoebiusMu[n/d](2^DivisorSigma[0, d] - 1))]; t = Union[ Table[ f[n], {n, 2^20}]]; Complement[ Take[t, 52], Table[2^i, {i, 0, 20}]]
Showing 1-3 of 3 results.
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