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A347882 Odd numbers k for which A003415(sigma(k^2))-(k^2) is strictly positive and a multiple of 3. Here A003415 is the arithmetic derivative. 6
273, 399, 651, 741, 777, 819, 903, 1197, 1209, 1281, 1365, 1407, 1443, 1533, 1659, 1677, 1767, 1925, 1953, 1995, 2035, 2037, 2109, 2163, 2223, 2289, 2331, 2379, 2451, 2457, 2613, 2667, 2709, 2847, 2919, 3003, 3081, 3171, 3255, 3297, 3423, 3441, 3477, 3591, 3627, 3685, 3705, 3783, 3801, 3819, 3843, 3885, 3999, 4017 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Of the first 200 terms of A097023, 44 appear also in this sequence, the first ones being 50281, 73535, 379953, etc. The square root of any hypothetical odd term appearing in A005820 should satisfy both conditions, and the term itself should appear in both A347383 and A347391.
LINKS
MATHEMATICA
ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); Select[Range[1, 4000, 2], (d = ad[DivisorSigma[1, #^2]] - #^2) > 0 && Divisible[d, 3] &] (* Amiram Eldar, Sep 18 2021 *)
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
isA347882(n) = if(!(n%2), 0, my(u=(A003415(sigma(n^2))-(n^2))); ((u>0)&&!(u%3)));
CROSSREFS
Subsequence of A347881. The intersection with A347887 gives A347888.
Cf. also A342923.
Sequence in context: A217004 A256638 A338557 * A347888 A306812 A157374
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 18 2021
STATUS
approved

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Last modified July 23 23:47 EDT 2024. Contains 374575 sequences. (Running on oeis4.)