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A324851
Numbers > 1 divisible by the sum of their prime indices.
19
2, 4, 6, 12, 15, 16, 20, 30, 35, 36, 42, 48, 56, 88, 99, 112, 120, 126, 130, 135, 143, 144, 160, 162, 180, 192, 210, 216, 220, 221, 228, 231, 242, 250, 256, 270, 275, 280, 288, 297, 300, 308, 322, 330, 338, 360, 396, 400, 408, 429, 435, 440, 455, 468, 480, 493
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. The sum of prime indices of n is A056239(n). For example, the prime indices of 99 are {2,2,5}, with sum 9, a divisor of 99, so 99 is in the sequence.
For any k>=2, let d be a divisor of k such that d > A056239(k). Then 2^(d-A056239(k))*k is in the sequence. Similarly if k is in the sequence with d = A056239(k), then 2^d*k is in the sequence. - Robert Israel, Mar 19 2019
LINKS
EXAMPLE
The sequence of terms together with their prime indices begins:
2: {1}
4: {1,1}
6: {1,2}
12: {1,1,2}
15: {2,3}
16: {1,1,1,1}
20: {1,1,3}
30: {1,2,3}
35: {3,4}
36: {1,1,2,2}
42: {1,2,4}
48: {1,1,1,1,2}
56: {1,1,1,4}
88: {1,1,1,5}
99: {2,2,5}
112: {1,1,1,1,4}
120: {1,1,1,2,3}
126: {1,2,2,4}
130: {1,3,6}
135: {2,2,2,3}
MAPLE
filter:= proc(n) local t; n mod add(numtheory:-pi(t[1])*t[2], t=ifactors(n)[2]) = 0 end proc:
select(filter, [$1..1000]); # Robert Israel, Mar 19 2019
MATHEMATICA
Select[Range[2, 100], Divisible[#, Plus@@Cases[If[#==1, {}, FactorInteger[#]], {p_, k_}:>PrimePi[p]*k]]&]
PROG
(PARI) isok(n) = {my(f = factor(n)); (n!=1) && !(n % sum(k=1, #f~, primepi(f[k, 1])*f[k, 2])); } \\ Michel Marcus, Mar 19 2019
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 18 2019
STATUS
approved