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A325793
Positive integers whose number of divisors is equal to their sum of prime indices.
13
3, 10, 28, 66, 70, 88, 208, 228, 306, 340, 364, 490, 495, 525, 544, 550, 675, 744, 870, 966, 1160, 1216, 1242, 1254, 1288, 1326, 1330, 1332, 1672, 1768, 1785, 1870, 2002, 2064, 2145, 2295, 2457, 2900, 2944, 3250, 3280, 3430, 3468, 3540, 3724, 4125, 4144, 4248
OFFSET
1,1
COMMENTS
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).
LINKS
EXAMPLE
The term 70 is in the sequence because it has 8 divisors {1, 2, 5, 7, 10, 14, 35, 70} and its sum of prime indices is also 1 + 3 + 4 = 8.
The sequence of terms together with their prime indices begins:
3: {2}
10: {1,3}
28: {1,1,4}
66: {1,2,5}
70: {1,3,4}
88: {1,1,1,5}
208: {1,1,1,1,6}
228: {1,1,2,8}
306: {1,2,2,7}
340: {1,1,3,7}
364: {1,1,4,6}
490: {1,3,4,4}
495: {2,2,3,5}
525: {2,3,3,4}
544: {1,1,1,1,1,7}
550: {1,3,3,5}
675: {2,2,2,3,3}
744: {1,1,1,2,11}
870: {1,2,3,10}
966: {1,2,4,9}
MAPLE
filter:= proc(n) local F, t;
F:= ifactors(n)[2];
add(numtheory:-pi(t[1])*t[2], t=F) = mul(t[2]+1, t=F)
end proc:
select(filter, [$1..10000]); # Robert Israel, Oct 16 2023
MATHEMATICA
Select[Range[100], DivisorSigma[0, #]==Total[Cases[FactorInteger[#], {p_, k_}:>PrimePi[p]*k]]&]
CROSSREFS
Positions of 0's in A325794.
Contains A239885 except for 1.
Sequence in context: A262724 A059193 A226863 * A325800 A037167 A267707
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 23 2019
STATUS
approved