A381548
Numbers k such that k and k+1 both have an odd number of abundant divisors.
Original entry on oeis.org
5984, 7424, 21735, 27404, 43064, 56924, 76544, 82004, 89775, 109395, 144584, 158235, 164835, 165375, 174824, 222704, 266475, 271215, 300104, 311024, 322335, 326655, 326864, 334304, 347984, 350175, 371924, 387584, 393855, 414315, 442035, 445004, 447524, 477224
Offset: 1
5984 is a term since it has 9 abundant divisors (88, 176, 272, 352, 544, 748, 1496, 2992, 5984) and 5984 + 1 = 5985 has one abundant divisor (5985 itself).
21735 is a term since it has 3 abundant divisors (945, 7245, 21735) and 21735 + 1 = 21736 has 9 abundant divisors (88, 104, 572, 836, 1144, 1672, 1976, 10868, 21736).
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q[n_] := q[n] = OddQ[DivisorSum[n, 1 &, DivisorSigma[-1, #] > 2 &]]; Select[Range[500000], q[#] && q[#+1] &]
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is1(k) = sumdiv(k, d, (sigma(d, -1) > 2)) % 2;
list(lim) = forstep(k = 3, lim, 2, if(is1(k), if(is1(k-1), print1(k-1, ", ")); if(is1(k+1), print1(k, ", "))));
A381547
Odd numbers with an odd number of abundant divisors.
Original entry on oeis.org
945, 1575, 2205, 3465, 4095, 4725, 5355, 5775, 5985, 6435, 6615, 6825, 7245, 7425, 8085, 8415, 8505, 8925, 9135, 9555, 9765, 10395, 11025, 11655, 12285, 12705, 12915, 13545, 14175, 14805, 15015, 16065, 16695, 17955, 18585, 19215, 19635, 19845, 21105, 21735, 21945
Offset: 1
945 is a term since it is odd, and it has only one abundant divisor, 945 itself.
4725 is a term since it is odd, and it has 3 abundant divisors, 945, 1575 and 4725.
14175 is a term since it is odd, and it has 5 abundant divisors, 945, 1575, 2835, 4725 and 14175.
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q[n_] := OddQ[DivisorSum[n, 1 &, DivisorSigma[-1, #] > 2 &]]; Select[Range[1, 22000, 2], q]
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isok(k) = if(k % 2, sumdiv(k, d, (sigma(d, -1) > 2)) % 2, 0);
A381549
Numbers k such that k, k+1 and k+2 all have an odd number of abundant divisors.
Original entry on oeis.org
96236031968, 229687160624, 274957745984, 331240852304, 363015363248, 386136575824, 407374391150, 623810538350, 734609097584, 745885389248, 1080953007848
Offset: 1
96236031968 is a term since it has 7 abundant divisors (992, 512368, 1024736, 46580848, 93161696, 48118015984, 96236031968), 96236031968 + 1 = 96236031969 has 9 abundant divisors (7857927, 10025631, 12641013, 290743299, 2600973837, 3318483861, 4184175303, 5660943057, 96236031969), and 96236031968 + 2 = 96236031970 has one abundant divisor (96236031970 itself).
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q[n_] := q[n] = OddQ[DivisorSum[n, 1 &, DivisorSigma[-1, #] > 2 &]]; With[{v = Import["https://oeis.org/A096536/b096536.txt", "Table"][[;; , 2]]}, Select[v, q[#] && q[# + 1] && q[# + 2] &]]
Showing 1-3 of 3 results.
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