A353061 Zumkeller numbers (A083207) that are not practical numbers (A005153).

70, 102, 114, 138, 174, 186, 222, 246, 258, 282, 318, 350, 354, 366, 372, 402, 426, 438, 444, 474, 490, 492, 498, 516, 534, 550, 564, 572, 582, 606, 618, 636, 642, 650, 654, 678, 708, 732, 762, 770, 786, 804, 822, 834, 836, 852, 876, 894, 906, 910, 940, 942, 945, 948, 978, 996

Offset: 1

Author

Jianing Song, Apr 20 2022

Keywords

• nonn

Comments

Different from A007621: A007621 contains no odd numbers, while every odd term in A083207 is here. The numbers 738, 748, 774, 846, ... are in A007621 and are not here.

But the subsequence of even terms (A005843 intersect this sequence) is a subsequence of A007621:

- A007621 = A173490 \ A007620;

- A005843 intersect this sequence = (A005843 intersect A083207) \ A005153;

- A083207 is a subsequence of A023196, and every perfect number is practical;

- So, (A005843 intersect A083207) \ A005153 is a subsequence of A173490, and A005153 is a supersequence of A007620.

Examples

			70 is a term since 70 is a Zumkeller number but not a practical number: 1+5+7+10+14+35 = 2+70, so 70 is a Zumkeller number; but 4 cannot be written as a sum of distinct divisors of 70, so 70 is not practical.
		

Links

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

Crossrefs

Cf. A083207, A005153, A007621.

Cf. also A173490, A007620, A023196, A005843.

Programs

PARI

isA353061(n) = is(n) && !is_A005153(n) \\ See A083207 for is(n) and A005153 for is_A005153(n)