A361387 Infinitary arithmetic numbers k whose mean infinitary divisor is an infinitary divisor of k.
1, 6, 60, 270, 420, 630, 2970, 5460, 8190, 36720, 136500, 172900, 204750, 245700, 491400, 790398, 791700, 819000, 1037400, 1138320, 1187550, 1228500, 1801800, 2457000, 3767400, 4176900, 4504500, 5405400, 6397300, 6688500, 6741630, 7698600, 8353800, 10032750, 10228680
Offset: 1
Keywords
Examples
6 is a term since the arithmetic mean of its infinitary divisors, {1, 2, 3, 6}, is 3, and 3 is also an infinitary divisor of 6.
60 is a term since the arithmetic mean of its infinitary divisors, {1, 3, 4, 5, 12, 15, 20, 60}, is 15, and 15 is also an infinitary divisor of 60.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..135
Crossrefs
Programs
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Mathematica
idivs[1] = {1}; idivs[n_] := Sort@ Flatten@ Outer[Times, Sequence @@ (FactorInteger[n] /. {p_, e_Integer} :> p^Select[Range[0, e], BitOr[e, #] == e &])]; Select[Range[10^5], IntegerQ[(r = Mean[(i = idivs[#])])] && MemberQ[i, r] &] -
PARI
isidiv(d, f) = {if (d==1, return (1)); for (k=1, #f~, bne = binary(f[k, 2]); bde = binary(valuation(d, f[k, 1])); if (#bde < #bne, bde = concat(vector(#bne-#bde), bde)); for (j=1, #bne, if (! bne[j] && bde[j], return (0)); ); ); return (1); } \\ Michel Marcus at A077609 is(n) = {my(f = factor(n), b, r); r = prod(i=1, #f~, b = binary(f[i, 2]); prod(k=1, #b, if(b[k], (f[i, 1]^(2^(#b-k))+1)/2, 1))); denominator(r) == 1 && n%r==0 && isidiv(r, f); }
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