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A347888 Odd numbers k for which A003415(sigma(k^2))-(k^2) is strictly positive and a multiple of six. Here A003415 is the arithmetic derivative. 2
273, 399, 651, 741, 903, 1209, 1407, 1533, 1659, 1677, 1767, 2037, 2163, 2331, 2451, 2457, 2613, 2667, 2847, 3003, 3081, 3297, 3423, 3591, 3685, 3783, 3819, 3843, 3885, 3999, 4017, 4095, 4161, 4179, 4329, 4345, 4389, 4431, 4503, 4683, 4953, 5061, 5187, 5529, 5691, 5817, 5859, 5871, 5985, 6123, 6231, 6279, 6327, 6357 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A square root of any hypothetical odd term x (if such numbers exist) in A005820 (triperfect numbers) should be a member of this sequence. See comments in A347882, A347887 and also in A347870 and in A347391.
Of the first 200 terms of A097023, 44 appear also in this sequence, the first ones being 50281, 73535, 379953, etc.
LINKS
MATHEMATICA
ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); Select[Range[1, 6500, 2], (d = ad[DivisorSigma[1, #^2]] - #^2) > 0 && Divisible[d, 6] &] (* Amiram Eldar, Sep 19 2021 *)
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
isA347888(n) = if(!(n%2), 0, my(u=(A003415(sigma(n^2))-(n^2))); ((u>0)&&!(u%6)));
CROSSREFS
Intersection of A347882 and A347887. Subsequence of A347881 and of A347885.
Sequence in context: A256638 A338557 A347882 * A306812 A157374 A043467
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 19 2021
STATUS
approved

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Last modified June 13 10:24 EDT 2024. Contains 373383 sequences. (Running on oeis4.)