OFFSET
1,1
COMMENTS
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
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]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 23 2019
STATUS
approved