OFFSET
1,1
COMMENTS
Numbers with k >= 4 prime factors (with multiplicity) that are congruent to 3 mod 4, no k-1 of which are equal. - Charlie Neder, Nov 03 2018
LINKS
Eric M. Schmidt, Table of n, a(n) for n = 1..10000
EXAMPLE
2205 is in S = {1,5,9, ... 4i+1, ...}, 2205 = 5*9*49 = 5*21^2; 5, 9, 21 and 49 are S-primes (A057948).
PROG
(Sage)
def A057949_list(bound) :
numterms = (bound-1)//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 S-prime
# 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]
# Eric M. Schmidt, Dec 11 2016
(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
Jud McCranie, Oct 14 2000
EXTENSIONS
Offset corrected by Eric M. Schmidt, Dec 11 2016
STATUS
approved