A337935 - OEIS

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

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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).