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

1,1

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, ...

Links

Table of n, a(n) for n=1..68.

Wikipedia, Contraharmonic mean

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A078174, A246655 (subsequence).

Sequence in context: A363727 A329366 A144711 * A036116 A246655 A000961

Adjacent sequences: A337932 A337933 A337934 * A337936 A337937 A337938

Keyword

nonn

Author

Ivan N. Ianakiev, Oct 01 2020

Status

approved