cp's OEIS Frontend

A325694 Numbers with one fewer divisors than the sum of their prime indices.

%I A325694 #5 May 28 2019 19:38:25
%S A325694 5,9,14,15,44,45,50,78,104,105,110,135,196,225,272,276,342,380,405,
%T A325694 476,572,585,608,650,693,726,735,825,888,930,968,1125,1215,1218,1240,
%U A325694 1472,1476,1482,1518,1566,1610,1624,1976,1995,2024,2090,2210,2256,2565,2618
%N A325694 Numbers with one fewer divisors than the sum of their prime indices.
%C A325694 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, with sum A056239(n).
%C A325694 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of the partitions counted by A325836.
%e A325694 The sequence of terms together with their prime indices begins:
%e A325694      5: {3}
%e A325694      9: {2,2}
%e A325694     14: {1,4}
%e A325694     15: {2,3}
%e A325694     44: {1,1,5}
%e A325694     45: {2,2,3}
%e A325694     50: {1,3,3}
%e A325694     78: {1,2,6}
%e A325694    104: {1,1,1,6}
%e A325694    105: {2,3,4}
%e A325694    110: {1,3,5}
%e A325694    135: {2,2,2,3}
%e A325694    196: {1,1,4,4}
%e A325694    225: {2,2,3,3}
%e A325694    272: {1,1,1,1,7}
%e A325694    276: {1,1,2,9}
%e A325694    342: {1,2,2,8}
%e A325694    380: {1,1,3,8}
%e A325694    405: {2,2,2,2,3}
%e A325694    476: {1,1,4,7}
%t A325694 Select[Range[1000],DivisorSigma[0,#]==Total[Cases[FactorInteger[#],{p_,k_}:>PrimePi[p]*k]]-1&]
%Y A325694 Positions of -1's in A325794.
%Y A325694 Cf. A000005, A056239, A112798, A325780, A325792, A325793, A325794, A325795, A325796, A325797, A325798, A325836.
%K A325694 nonn
%O A325694 1,1
%A A325694 _Gus Wiseman_, May 23 2019