

A057949


Numbers with more than one factorization into Sprimes. See A054520 and A057948 for definition.


9



441, 693, 1089, 1197, 1449, 1617, 1881, 1953, 2205, 2277, 2541, 2709, 2793, 2961, 3069, 3249, 3381, 3465, 3717, 3933, 3969, 4221, 4257, 4389, 4473, 4557, 4653, 4761, 4977, 5229, 5301, 5313, 5445, 5733, 5841, 5929, 5985, 6237, 6321, 6417, 6489, 6633
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OFFSET

1,1


COMMENTS

Numbers with k >= 4 prime factors (with multiplicity) that are congruent to 3 mod 4, no k1 of which are equal.  Charlie Neder, Nov 03 2018


LINKS



EXAMPLE

2205 is in S = {1,5,9, ... 4i+1, ...}, 2205 = 5*9*49 = 5*21^2; 5, 9, 21 and 49 are Sprimes (A057948).


PROG

(Sage)
numterms = (bound1)//4 + 1
M = [1] * numterms
for k in range(1, numterms) :
if M[k] == 1 :
kpower = k
while kpower < numterms :
step = 4*kpower+1
for j in range(kpower, numterms, step) :
M[j] *= 4*k+1
kpower = 4*kpower*k + kpower + k
# Now M[k] contains the product of the terms p^e where p is an Sprime
# and e is maximal such that p^e divides 4*k+1
return [4*k+1 for k in range(numterms) if M[k] > 4*k+1]
(PARI) ok(n)={if(n%4==1, my(f=factor(n)); my(s=[f[i, 2]  i<[1..#f~], f[i, 1]%4==3]); vecsum(s)>=4 && vecmax(s)<vecsum(s)1, 0)} \\ Andrew Howroyd, Nov 25 2018


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



