cp's OEIS Frontend

A360669 Nonprime numbers > 1 for which the prime indices have the same mean as their first differences.

%I A360669 #5 Feb 19 2023 18:02:39
%S A360669 10,39,68,115,138,259,310,328,387,517,574,636,793,795,1034,1168,1206,
%T A360669 1241,1281,1340,1534,1691,1825,2212,2278,2328,2343,2369,2370,2727,
%U A360669 2774,2905,3081,3277,3818,3924,4064,4074,4247,4268,4360,4539,4850,4905,5243,5335
%N A360669 Nonprime numbers > 1 for which the prime indices have the same mean as their first differences.
%C A360669 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%e A360669 The terms together with their prime indices begin:
%e A360669      1: {}
%e A360669     10: {1,3}
%e A360669     39: {2,6}
%e A360669     68: {1,1,7}
%e A360669    115: {3,9}
%e A360669    138: {1,2,9}
%e A360669    259: {4,12}
%e A360669    310: {1,3,11}
%e A360669    328: {1,1,1,13}
%e A360669    387: {2,2,14}
%e A360669    517: {5,15}
%e A360669    574: {1,4,13}
%e A360669    636: {1,1,2,16}
%e A360669 For example, the prime indices of 138 are {1,2,9}, with mean 4, and with first differences (1,7), with mean also 4, so 138 is in the sequence.
%t A360669 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A360669 Select[Range[2,1000],Mean[prix[#]]==Mean[Differences[prix[#]]]&]
%Y A360669 These partitions are counted by A360670.
%Y A360669 A058398 counts partitions by mean, see also A008284, A327482.
%Y A360669 A112798 = prime indices, length A001222, sum A056239, mean A326567/A326568.
%Y A360669 A124010 gives prime signature, mean A088529/A088530.
%Y A360669 A301987 lists numbers whose sum of prime indices equals their product.
%Y A360669 A316413 lists numbers whose prime indices have integer mean.
%Y A360669 A334201 adds up all prime indices except the greatest.
%Y A360669 A360614/A360615 = mean of first differences of 0-prepended prime indices.
%Y A360669 Cf. A340610, A344415, A348551, A359904, A360008, A360068, A360681.
%K A360669 nonn
%O A360669 1,1
%A A360669 _Gus Wiseman_, Feb 18 2023