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Multiply-perfect numbers: n divides sigma(n).
(Formerly M4182)
+10
188
1, 6, 28, 120, 496, 672, 8128, 30240, 32760, 523776, 2178540, 23569920, 33550336, 45532800, 142990848, 459818240, 1379454720, 1476304896, 8589869056, 14182439040, 31998395520, 43861478400, 51001180160, 66433720320, 137438691328, 153003540480, 403031236608
CROSSREFS
Other subsequences: A046985, A046986, A046987, A047728, A065997, A066289, ( A076231, A076233, A076234), A088844, A088845, A088846, A091443, A114887, A166069, A245782, A260508, A306667, ( A325021 U A325022), ( A325023 U A325024), ( A325025 U A325026), A325637, A323653, A330532, ( A330533 U A331724), A336702, A341045.
Denominator of (n / tau(n) - sigma(n) / n).
+10
6
1, 2, 6, 12, 10, 2, 14, 8, 9, 10, 22, 3, 26, 14, 20, 80, 34, 6, 38, 30, 84, 22, 46, 2, 75, 26, 108, 3, 58, 20, 62, 96, 44, 34, 140, 36, 74, 38, 156, 4, 82, 28, 86, 33, 30, 46, 94, 60, 147, 150, 68, 78, 106, 36, 220, 7, 228, 58, 118, 5, 122, 62, 126, 448, 260
Numerator of (n/tau(n) - sigma(n)/n).
+10
5
0, -1, 1, -5, 13, -1, 33, 1, 14, 7, 97, -1, 141, 25, 43, 101, 253, 5, 321, 37, 313, 85, 481, 1, 532, 127, 569, 8, 781, 27, 897, 323, 299, 235, 1033, 53, 1293, 301, 1297, 11, 1597, 83, 1761, 179, 173, 457, 2113, 133, 2230, 971, 771, 529, 2701, 163, 2737, 34, 2929, 751, 3361, 11, 3597, 865, 1115
Numbers n such that (n/tau(n) - sigma(n)/n) < 1.
+10
5
1, 2, 3, 4, 6, 8, 10, 12, 18, 24
Numbers n such that k(n) = n/tau(n) - sigma(n)/n is an integer.
+10
4
1, 672, 4680, 30240, 435708, 23569920, 45532800, 4138364160, 14182439040, 53798734080, 153003540480, 403031236608, 518666803200
COMMENTS
Refactorable multiply-perfect numbers ( A245782) are members of this sequence.
Numbers n such that k(n) = (n/tau(n) + sigma(n)/n) is an integer.
+10
3
1, 672, 4680, 30240, 23569920, 45532800, 275890944, 14182439040, 153003540480, 403031236608, 518666803200
COMMENTS
Refactorable multiply-perfect numbers ( A245782) are members of this sequence.
1, 20, 196, 368, 650, 672, 780, 836, 1888, 2352, 3192, 11096, 17816, 20496, 30240, 51060, 84660, 130304, 979992, 1848964, 2291936, 3767100, 4526272, 8353792, 15126992, 15287976, 23569920, 33468416, 45532800, 74899952, 381236216, 623799776, 712023296, 1845991216
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