

A337935


Numbers with integer contraharmonic mean of distinct prime factors.


0



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
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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: A059046 A329366 A144711 * A036116 A246655 A000961
Adjacent sequences: A337932 A337933 A337934 * A337936 A337937 A337938


KEYWORD

nonn


AUTHOR

Ivan N. Ianakiev, Oct 01 2020


STATUS

approved



