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%I #20 Nov 21 2020 11:27:58
%S 1,2,3,4,5,6,14,8,18,10,22,12,26,14,30,16,34,36,38,20,63,22,46,48,50,
%T 26,81,28,58,60,62,32,99,68,70,72,74,76,117,40,82,126,86,44,135,92,94,
%U 96,98,100,153,52,106,162,165,56,171,116,118,180,122,124,189,64,195,198,134,68,207,210
%N a(n) is the sum of all parts of all partitions of n into consecutive parts that differ by 5.
%C The one-part partition n = n is included in the count.
%F a(n) = n*A334541(n).
%e For n = 27 there are three partitions of 27 into consecutive parts that differ by 5, including 27 as a valid partition. They are [27], [16, 11] and [14, 9, 4]. The sum of all parts is [27] + [16 + 11] + [14 + 9 + 4] = 81, so a(27) = 81.
%Y Sequences of the same family where the parts differs by k are: A038040 (k=0), A245579 (k=1), A060872 (k=2), A334463 (k=3), A327262 (k=4), this sequence (k=5).
%Y Cf. A334465, A334541.
%K nonn
%O 1,2
%A _Omar E. Pol_, May 09 2020