A381548 Numbers k such that k and k+1 both have an odd number of abundant divisors.

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

Author

Amiram Eldar, Feb 26 2025

Keywords

• nonn

Comments

Numbers k such that k and k+1 are both in A381546.

Examples

			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).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A096399 and A381546.

Subsequences: A381549.

Programs

Mathematica

q[n_] := q[n] = OddQ[DivisorSum[n, 1 &, DivisorSigma[-1, #] > 2 &]]; Select[Range[500000], q[#] && q[#+1] &]

PARI

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, ", "))));