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A353061
Zumkeller numbers (A083207) that are not practical numbers (A005153).
1
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
1,1
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:
- 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.
LINKS
EXAMPLE
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.
PROG
(PARI) isA353061(n) = is(n) && !is_A005153(n) \\ See A083207 for is(n) and A005153 for is_A005153(n)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jianing Song, Apr 20 2022
STATUS
approved