A337935 Numbers with integer contraharmonic mean of distinct prime factors.

2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 190, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241

Offset: 1

Author

Ivan N. Ianakiev, Oct 01 2020

Keywords

• nonn

Comments

Similar sequences are A078174 (with respect to arithmetic mean) and A246655 (with respect to geometric mean).

Up to 10^6 there are 2637 terms that are not in A000961 (and in A246655). The list starts: 190, 380, 390, 615, 638, 710, 760, 780, 950, 1170, 1235, 1276, 1365, 1420, 1518, 1520, 1558, 1560, 1770, 1845, 1900, 1950, 2340, 2552, 2840, ...

Examples

			The distinct prime factors of 190 are {2,5,19} and their contraharmonic mean is (4+25+361)/(2+5+19) = 15. Therefore, 190 is a term.
		

Links

• Wikipedia, Contraharmonic mean

Crossrefs

Cf. A078174, A246655 (subsequence).

Programs

Mathematica

pf[n_]:=First/@FactorInteger[n];
Select[Range[2,241],IntegerQ[ContraharmonicMean[pf[#]]]&]

PARI

isok(m) = if (m>1, my(f=factor(m)); !(norml2(f[,1]) % vecsum(f[,1]))); \\ Michel Marcus, Oct 01 2020