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A215369 Numbers n with the same f-value as n+1, where f(n) = A056239(n) = Sum_{i} i*e_i for n = Product_{i} prime(i)^e_i.

%I A215369 #17 Mar 22 2017 10:23:49
%S A215369 3,5,9,14,21,27,44,77,98,104,115,125,152,247,289,363,423,455,492,624,
%T A215369 670,714,860,1016,1044,1224,1274,1449,1659,1715,1817,1862,2013,2255,
%U A215369 2261,2424,2596,2679,2847,3255,3285,3362,3477,3478,3626,3925,4185,4233,4292
%N A215369 Numbers n with the same f-value as n+1, where f(n) = A056239(n) = Sum_{i} i*e_i for n = Product_{i} prime(i)^e_i.
%C A215369 Also numbers n such that both n and n+1 are in the same row of A215366.
%H A215369 Alois P. Heinz, <a href="/A215369/b215369.txt">Table of n, a(n) for n = 1..1000</a>
%e A215369 44 is in the sequence because 44 = 2^2 * 11 = prime(1)^2 * prime(5) => f(44) = 1*2+5 = 7 and 44+1 = 45 = 3^2*5 = prime(2)^2 * prime(3) => f(45) = 2*2+3 = 7.
%p A215369 f:= n-> add(numtheory[pi](i[1])*i[2], i=ifactors(n)[2]):
%p A215369 a:= proc(n) option remember; local k;
%p A215369       for k from 1+ `if`(n=1, 0, a(n-1))
%p A215369       while f(k)<>f(k+1) do od; k
%p A215369     end:
%p A215369 seq(a(n), n=1..70);
%t A215369 f[n_] := Sum[PrimePi[i[[1]]]*i[[2]], {i, FactorInteger[n]}];
%t A215369 a[n_] := a[n] = (For[k = 1 + If[n==1, 0, a[n-1]], f[k] != f[k+1], k++]; k);
%t A215369 Array[a, 70] (* _Jean-François Alcover_, Mar 22 2017, translated from Maple *)
%Y A215369 Cf. A056239, A088850, A215366.
%K A215369 nonn
%O A215369 1,1
%A A215369 _Alois P. Heinz_, Aug 09 2012