A381549 Numbers k such that k, k+1 and k+2 all have an odd number of abundant divisors.

96236031968, 229687160624, 274957745984, 331240852304, 363015363248, 386136575824, 407374391150, 623810538350, 734609097584, 745885389248, 1080953007848

Offset: 1

Author

Amiram Eldar, Feb 26 2025

Keywords

• nonn
• more

Comments

a(11) > 10^12, if it exists.

Examples

			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).
		

Crossrefs

Subsequence of A096536, A381546 and A381548.

Programs

Mathematica

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] &]]

Extensions

a(11) from Jinyuan Wang, Mar 12 2025