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A325793
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Positive integers whose number of divisors is equal to their sum of prime indices.
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13
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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
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OFFSET
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1,1
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COMMENTS
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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).
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LINKS
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EXAMPLE
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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}
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MAPLE
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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:
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MATHEMATICA
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Select[Range[100], DivisorSigma[0, #]==Total[Cases[FactorInteger[#], {p_, k_}:>PrimePi[p]*k]]&]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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