A210976
Square array T(n,k), n>=1, k>=1, read by antidiagonals in which column k lists the positive integers whose number of divisors is not k.
Original entry on oeis.org
2, 3, 1, 4, 4, 1, 5, 6, 2, 1, 6, 8, 3, 2, 1, 7, 9, 5, 3, 2, 1, 8, 10, 6, 4, 3, 2, 1, 9, 12, 7, 5, 4, 3, 2, 1, 10, 14, 8, 7, 5, 4, 3, 2, 1, 11, 15, 10, 9, 6, 5, 4, 3, 2, 1, 12, 16, 11, 11, 7, 6, 5, 4, 3, 2, 1, 13, 18, 12, 12, 8, 7, 6, 5, 4, 3, 2, 1, 14, 20
Offset: 1
Column 2 lists the nonprimes A018252 because they are the positive integers whose number of divisors is not 2.
Array begins:
2, 1, 1, 1, 1, 1, 1, 1, 1, 1,
3, 4, 2, 2, 2, 2, 2, 2, 2,
4, 6, 3, 3, 3, 3, 3, 3,
5, 8, 5, 4, 4, 4, 4,
6, 9, 6, 5, 5, 5,
7, 10, 7, 7, 6,
8, 12, 8, 9,
9, 14, 10,
10, 15,
11,
A213367
Numbers that are not squares of primes.
Original entry on oeis.org
1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70
Offset: 1
4 is not in the sequence because 4 as three divisors: 1, 2, 4.
A278474
Numbers n such that the product of proper divisors of n ends with n and n is not a multiplicatively perfect number (A007422).
Original entry on oeis.org
24, 36, 76, 375, 376, 432, 624, 625, 693, 875, 999, 2499, 4557, 8307, 9375, 9376, 9999, 34375, 40625, 47943, 50001, 59375, 81249, 90624, 90625, 99999, 109376, 186432, 218751, 586432, 609375, 690624, 718751, 781249, 890625, 954193, 968751, 999999, 2109375, 2890624, 2890625
Offset: 1
24 is in the sequence because 24 has 7 proper divisors {1,2,3,4,6,8,12} and 1*2*3*4*6*8*12 = 13824;
36 is in the sequence because 36 has 8 proper divisors {1,2,3,4,6,9,12,18} and 1*2*3*4*6*9*12*18 = 279936;
76 is in the sequence because 76 has 5 proper divisors {1,2,4,19,38} and 1*2*4*19*38 = 5776, etc.
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Select[Range[3000000], Mod[Sqrt[#1]^DivisorSigma[0, #1]/#1, 10^IntegerLength[#1]] == #1 && Sqrt[#1]^DivisorSigma[0, #1] != #1^2 & ]
Showing 1-3 of 3 results.
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