A057949 Numbers with more than one factorization into S-primes. See A054520 and A057948 for definition.
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
Offset: 1
Keywords
Examples
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).
Links
- Eric M. Schmidt, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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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) -
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
Extensions
Offset corrected by Eric M. Schmidt, Dec 11 2016
Comments