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A355541
Numbers k such that A061201(k) is divisible by k.
0
1, 2, 7, 31, 1393, 5012, 7649, 50235, 147296, 426606, 611769, 3491681, 9324642, 11815109, 53962364, 82680301, 96789197, 230882246, 378444764, 1489280093, 1489280606, 3651325650, 5891877914, 5891877947, 5891877966, 58604540872
OFFSET
1,2
COMMENTS
Numbers k such that the mean value of A007425 over the range 1..k is an integer.
The corresponding quotients are 1, 2, 4, 9, 32, 43, 47, 67, 80, 94, 99, 125, 141, 145, 172, 180, 183, 200, 210, 239, 239, 259, 270, 270, 270, 326, ... .
a(27) > 7.5*10^10, if it exists.
EXAMPLE
7 is a term since A061201(7) = 28 = 4 * 7 is divisible by 7.
MATHEMATICA
f[p_, e_] := (e+1)*(e+2)/2; d3[1] = 1; d3[n_] := Times @@ f @@@ FactorInteger[n]; sum = 0; seq = {}; Do[sum += d3[n]; If[Divisible[sum, n], AppendTo[seq, n]], {n, 1, 10^6}]; seq
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Jul 06 2022
STATUS
approved